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# Why coherence measure monotonicity under selective incoherent operation should be form $C\left( \rho \right) \ge \sum_n{p_nC\left( \rho _n \right)}$?

In this paper, the authors give four postulates if a function $$C$$ can be taken as a coherence measure:

(C1) $$C(\rho) \geqslant 0$$, and $$C(\rho)=0$$ if and only if $$\rho \in \mathcal{I}$$, where $$\mathcal{I}$$ stands for sets of incoherent states.

(C2a) Monotonicity under incoherent operations, $$C(\rho) \geqslant$$ $$C(\Lambda(\rho))$$ if $$\Lambda$$ is an incoherent operation.

(C2b) Monotonicity under selective incoherent operations, $$C(\rho) \geqslant \sum_{n} p_{n} C\left(\rho_{n}\right)$$, where $$p_{n}=\operatorname{Tr}\left(K_{n} \rho K_{n}^{\dagger}\right), \rho_{n}=$$ $$K_{n} \rho K_{n}^{\dagger} / p_{n}$$, and $$\Lambda(\rho)=\sum_{n} K_{n} \rho K_{n}^{\dagger}$$ is an incoherent operation.

(C3) Nonincreasing under mixing of quantum states, i.e., convexity, $$\sum_{n} p_{n} C\left(\rho_{n}\right) \geqslant C\left(\sum_{n} p_{n} \rho_{n}\right)$$ for any set of states $$\left\{\rho_{n}\right\}$$ and any probability distribution $$\left\{p_{n}\right\}$$.

My question is about (C2b). Since they require $$K_n \mathcal{I} K_n^\dagger\subset \mathcal{I},\forall n$$, so why should (C2b) be $$C\left( \rho \right) \ge \sum_n{p_nC\left( \rho _n \right)}$$ instead of $$C\left( \rho \right) \ge C\left( \rho _n \right) ,\forall n$$?

• Why not to ask the paper's authors? Aug 4 at 9:24
• Interestingly, I think that $C(\rho) \geq C(\rho_n), \forall n$ is satisfied by the $l_1$-monotone for qubits.
– R.W
Aug 5 at 8:22

These conditions aren't really related to coherence theory per se, they are directly inspired by the requirements that entanglement measures are typically required to satisfy, see e.g. the old review on entanglement measures.

The reason why the stronger condition $$C(\rho) \geq C(\rho_n)$$ is not imposed is simply that this would rule out the vast majority of coherence/entanglement measures – coherence or entanglement, as measured by standard monotones such as the entropy, can actually be increased with some probability even under an incoherent/LOCC operation.

An explicit example can be found in Bennett et al.'s Procrustean protocol for entanglement concentration, with the relevant quote being as follows:

[...] we note that the measurement of $$k$$ occasionally yields a residual state $$\Psi_k$$ with more entropy of entanglement than the original state $$\Psi$$. However, neither the measurement of $$k$$ nor any other local processing by one or both parties can increase the expected entropy of entanglement between Alice’s and Bob’s subsystems.


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Contents

category theory

Contents

Idea

The concept of a (left/right) cancellative category is the generalization of the concept of (left/right) cancellative monoid from monoids to categories.

Definition

In category theory, “left cancellative” is a synonym for all arrows are monic. Thus the typical way for left cancellative categories to be constructed to take a category $C$ and then restrict to a class of monomorphisms closed under composition, such as all monomomorphisms, or regular monomorphisms if the category is regular, etc.

In fact every left cancellative $C$ arises this way (in the tautological sense of applying this consideration to $C$ itself): a category $\mathcal{C}$ being left cancellative means all its morphisms are monos.

Equivalently, for arbitrary morphisms $f,h_0,h_1$ of $\mathcal{C}$, if $f\circ h_0=f\circ h_1$, then $h_0=h_1$.

Examples

Tautological examples:

Non-tautological examples:

References

• M. V. Lawson and A. R. Wallis, A categorical description of Bass-Serre theory (arXiv:1304.6854v5)

• M. V. Lawson, “Ordered Groupoids and Left Cancellative Categories” Semigroup Forum, Volume 68, Issue 3, (2004), 458–-476

Last revised on May 23, 2021 at 13:53:16. See the history of this page for a list of all contributions to it.

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### Higher Spin Dark Matter

Little is known about dark matter beyond the fact that it does not interact with the standard model or itself, or else does so incredibly weakly. A natural candidate, given the history of no-go theorems against their interactions, are higher spin fields. Here we develop the scenario of higher spin (spin $s>2$) dark matter. We show that the gravitational production of superheavy bosonic higher spin fields during inflation can provide all the dark matter we observe today. We consider the observable signatures, and find a potential characteristic signature of bosonic higher spin dark matter in directional direct detection; we find that there are distinct spin-dependent contributions to the double differential recoil rate, which complement the oscillatory imprint of higher spin fields in the cosmic microwave background. We consider the extension to higher spin fermions and supersymmetric higher spins.

### A Closer Look at CP-Violating Higgs Portal Dark Matter as a Candidate for the GCE

A statistically significant excess of gamma rays has been reported and robustly confirmed in the Galactic Center over the past decade. Large local dark matter densities suggest that this Galactic Center Excess (GCE) may be attributable to new physics, and indeed it has been shown that this signal is well-modelled by annihilations dominantly into $b\bar{b}$ with a WIMP-scale cross section. In this paper, we consider Majorana dark matter annihilating through a Higgs portal as a candidate source for this signal, where a large CP-violation in the Higgs coupling may serve to severely suppress scattering rates. In particular, we explore the phenomenology of two minimal UV completions, a singlet-doublet model and a doublet-triplet model, and map out the available parameter space which can give a viable signal while respecting current experimental constraints.

### The physics case for an electron muon collider

An electron muon collider is proposed here targeting at multi-ab$^{-1}$ integrated luminosities at various stages, involving asymmetrical collision profile of, e.g., 20-200 GeV, 50-1000 GeV and 100-3000 GeV for the electron and muon beam energy, respectively. This novel collider can serve as a powerful machine to probe lepton flavor violation and measure Higgs boson properties precisely. The collision of an electron and a muon beam leads to less physics backgrounds compared with either an electron-electron or a muon-muon beam, as physics processes appear mostly through vector boson fusion or scattering. The asymmetrical beam energy tends to have collision products boosted towards the electron beam side, which can be exploited to reduce beam-induced background from muon beam upstream to a large extent.


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# Browse Dissertations and Theses - Mathematics by Subject "Jet spaces"

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For $k,n\ge 1$, the jet space $J^k(\R^n)$ is the set of $k^{th}$-order Taylor polynomials of functions in $C^k(\R^n)$. Warhurst constructs a Carnot group structure on $J^k(\R^n)$ such that the jets of functions in ...

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## Journal of Statistical Mechanics: Theory and Experiment

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2007
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2020
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2020
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2016
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2010
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2013
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2004
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2004
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2006
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2007
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Which is more effective for suppressing an infectious disease: imperfect vaccination or defense against contagion? Zbl 1459.92056
Kuga, Kazuki; Tanimoto, Jun
2018
Entanglement Hamiltonian and entanglement contour in inhomogeneous 1D critical systems. Zbl 1459.81022
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2018
Comparing dynamics: deep neural networks versus glassy systems. Zbl 1459.82317
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Integrable quenches in nested spin chains. II: Fusion of boundary transfer matrices. Zbl 1457.82040
Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale; Pozsgay, Balázs
2019
Entanglement entropy of two disjoint intervals from fusion algebra of twist fields. Zbl 1456.81399
Rajabpour, M. A.; Gliozzi, F.
2012
Entanglement contour. Zbl 1456.81053
Chen, Yangang; Vidal, Guifre
2014
Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids. Zbl 1456.81080
Laflorencie, Nicolas; Rachel, Stephan
2014
Entanglement negativity after a global quantum quench. Zbl 1456.81055
Coser, Andrea; Tonni, Erik; Calabrese, Pasquale
2014
Bethe ansatz for the Temperley-Lieb loop model with open boundaries. Zbl 1145.82320
de Gier, Jan; Pyatov, Pavel
2004
Stochastic interacting particle systems out of equilibrium. Zbl 1456.82649
Bertini, L.; De Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.
2007
A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle. Zbl 1457.82251
2019
Symmetry resolved entanglement: exact results in 1D and beyond. Zbl 1456.81064
Fraenkel, Shachar; Goldstein, Moshe
2020
Large deviations for the Kardar-Parisi-Zhang equation from the Kadomtsev-Petviashvili equation. Zbl 1457.82362
Le Doussal, Pierre
2020
One-boundary Temperley-Lieb algebras in the XXZ and loop models. Zbl 1459.82054
Nichols, A.; Rittenberg, V.; de Gier, J.
2005
Holomorphic parafermions in the Potts model and stochastic Loewner evolution. Zbl 1456.82176
Riva, V.; Cardy, J.
2006
On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary. Zbl 1244.81035
Doikou, Anastasia; Martin, Paul P.
2006
Eigenstate thermalization hypothesis in conformal field theory. Zbl 1459.81083
Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong
2018
Current fluctuations in periodically driven systems. Zbl 1459.82131
Barato, Andre C.; Chetrite, Raphael
2018
Entanglement entropy of excited states. Zbl 1456.82216
Alba, Vincenzo; Fagotti, Maurizio; Calabrese, Pasquale
2009
Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson localization models. Zbl 07330673
Monthus, Cécile
2021
Exact quantization conditions for cluster integrable systems. Zbl 1456.82356
Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
2016
Thermal form-factor approach to dynamical correlation functions of integrable lattice models. Zbl 1457.82071
Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Kozlowski, Karol K.; Suzuki, Junji
2017
Promoting cooperation by reputation-driven group formation. Zbl 1456.91023
Yang, Han-Xin; Wang, Zhen
2017
A new attempt to identify long-term precursors for endogenous financial crises in the market correlation structures. Zbl 07531149
Heckens, Anton J.; Guhr, Thomas
2022
Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson localization models. Zbl 07330673
Monthus, Cécile
2021
Localization transition in the discrete nonlinear Schrödinger equation: ensembles inequivalence and negative temperatures. Zbl 07330571
Gradenigo, Giacomo; Iubini, Stefano; Livi, Roberto; Majumdar, Satya N.
2021
Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets. Zbl 07330660
Monthus, Cécile
2021
Deep double descent: where bigger models and more data hurt. Zbl 07451713
Nakkiran, Preetum; Kaplun, Gal; Bansal, Yamini; Yang, Tristan; Barak, Boaz; Sutskever, Ilya
2021
Asymptotic analysis of the elephant random walk. Zbl 07330544
Coletti, Cristian F.; Papageorgiou, Ioannis
2021
Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models. Zbl 07382827
Monthus, Cécile
2021
Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates. Zbl 07400666
Monthus, Cécile
2021
Current operators in integrable models: a review. Zbl 07400677
Borsi, Márton; Pozsgay, Balázs; Pristyák, Levente
2021
Survival probability of a run-and-tumble particle in the presence of a drift. Zbl 1489.82035
De Bruyne, Benjamin; Majumdar, Satya N.; Schehr, Grégory
2021
Optimization and growth in first-passage resetting. Zbl 07330542
De Bruyne, B.; Randon-Furling, J.; Redner, S.
2021
Reputation preferences resolve social dilemmas in spatial multigames. Zbl 07330562
Li, Xiaopeng; Hao, Gang; Wang, Huaibin; Xia, Chengyi; Perc, Matjaž
2021
Gradient descent dynamics in the mixed $$p$$-spin spherical model: finite-size simulations and comparison with mean-field integration. Zbl 07330672
Folena, Giampaolo; Franz, Silvio; Ricci-Tersenghi, Federico
2021
Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps. Zbl 07400669
Monthus, Cécile
2021
Superdiffusion in spin chains. Zbl 07400670
Bulchandani, Vir B.; Gopalakrishnan, Sarang; Ilievski, Enej
2021
Inference of Markov models from trajectories via large deviations at level 2.5 with applications to random walks in disordered media. Zbl 07399560
Monthus, Cécile
2021
Stochastic dynamics and superstatistics of the many-particle kappa distribution. Zbl 07398335
Gravanis, E.; Akylas, E.; Livadiotis, G.
2021
Scaling domains in the nonequilibrium athermal random field Ising model of finite systems. Zbl 07330541
Janićević, Sanja; Knežević, Dragica; Mijatović, Svetislav; Spasojević, Djordje
2021
Surfing on minima of isostatic landscapes: avalanches and unjamming transition. Zbl 07330576
Franz, Silvio; Sclocchi, Antonio; Urbani, Pierfrancesco
2021
Cramér moderate deviations for the elephant random walk. Zbl 07330579
Fan, Xiequan; Hu, Haijuan; Ma, Xiaohui
2021
Traffic dynamics of uni- and bidirectional pedestrian flows including dyad social groups in a ring-shaped corridor. Zbl 07330583
Ye, Rui; Fang, Zhiming; Lian, Liping; Wang, Qiao; Zeng, Guang; Cao, Shuchao; Zhang, Jun; Song, Weiguo
2021
Stochastic bifurcation for two-time-scale dynamical system with $$\alpha$$-stable Lévy noise. Zbl 07330663
Yuan, Shenglan; Zeng, Zhigang; Duan, Jinqiao
2021
Heterogeneity and Superspreading effect on herd immunity. Zbl 07330678
Oz, Yaron; Rubinstein, Ittai; Safra, Muli
2021
Free energy fluxes and the kubo-Martin-Schwinger relation. Zbl 07356465
Doyon, Benjamin; Durnin, Joseph
2021
Generalisation error in learning with random features and the hidden manifold model. Zbl 07451723
Gerace, Federica; Loureiro, Bruno; Krzakala, Florent; Mézard, Marc; Zdeborová, Lenka
2021
Form factors and generalized hydrodynamics for integrable systems. Zbl 07430625
Cubero, Axel Cortés; Yoshimura, Takato; Spohn, Herbert
2021
Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects. Zbl 07430636
Alba, Vincenzo; Bertini, Bruno; Fagotti, Maurizio; Piroli, Lorenzo; Ruggiero, Paola
2021
Exact quench dynamics of symmetry resolved entanglement in a free fermion chain. Zbl 07414192
Parez, Gilles; Bonsignori, Riccarda; Calabrese, Pasquale
2021
The phase diagram of ultra quantum liquids. Zbl 07330538
Son, Dam Thanh; Stephanov, Mikhail; Yee, Ho-Ung
2021
Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition. Zbl 07330545
Chaudhuri, Debasish; Dhar, Abhishek
2021
The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models. Zbl 07330549
Panfil, Miłosz
2021
Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement. Zbl 07330553
Mallmin, E.; Blythe, Richard A.; Evans, Martin R.
2021
Steady state entropy production rate for scalar Langevin field theories. Zbl 07330555
Li, Yuting I.; Cates, Michael E.
2021
Out-of-equilibrium Frenkel-Kontorova model. Zbl 07330558
Imparato, A.
2021
Axiomatic tests for the Boltzmann distribution. Zbl 07330565
Cerreia-Vioglio, Simone; Maccheroni, Fabio; Marinacci, Massimo; Rustichini, Aldo
2021
Sum rules for the supersymmetric eight-vertex model. Zbl 07330568
Brasseur, Sandrine; Hagendorf, Christian
2021
Approximate Fokker-Planck-Kolmogorov equation analysis for asymmetric multistable energy harvesters excited by white noise. Zbl 07330584
Wang, Wei; Cao, Junyi; Wei, Zon-Han; Litak, Grzegorz
2021
Notes about the macroscopic fluctuating theory. Zbl 07330585
Garrido, P. L.
2021
Pushing run-and-tumble particles through a rugged channel. Zbl 07330665
Bijnens, Bram; Maes, Christian
2021
Tuning Ginzburg-Landau theory to quantitatively study thin ferromagnetic materials. Zbl 07330670
Guruciaga, Pamela C.; Caballero, Nirvana; Jeudy, Vincent; Curiale, Javier; Bustingorry, Sebastian
2021
Effect of transcription reinitiation in stochastic gene expression. Zbl 07330680
Karmakar, Rajesh; Das, Amit Kumar
2021
Groundstate finite-size corrections and dilogarithm identities for the twisted $$A_1^{({1})}, {A}_{2}^{(1)}$$ and $$A_{2}^{(2)}$$ models. Zbl 07356438
Morin-Duchesne, Alexi; Klümper, Andreas; Pearce, Paul A.
2021
Fundamental diagram of pedestrian flow including wheelchair users in straight corridors. Zbl 07356451
Pan, Hongliang; Zhang, Jun; Song, Weiguo; Yao, Bin
2021
Superspreaders and high variance infectious diseases. Zbl 07356457
Oz, Yaron; Rubinstein, Ittai; Safra, Muli
2021
Fluctuation-dissipation relations in the absence of detailed balance: formalism and applications to active matter. Zbl 07356460
Cengio, Sara Dal; Levis, Demian; Pagonabarraga, Ignacio
2021
Coherent spin states and stochastic hybrid path integrals. Zbl 07356466
Bressloff, Paul C.
2021
A new measure between sets of probability distributions with applications to erratic financial behavior. Zbl 07451709
James, Nick; Menzies, Max
2021
Triple descent and the two kinds of overfitting: where and why do they appear? Zbl 07451712
d’Ascoli, Stéphane; Sagun, Levent; Biroli, Giulio
2021
A random matrix analysis of random Fourier features: beyond the Gaussian kernel, a precise phase transition, and the corresponding double descent. Zbl 07451716
Liao, Zhenyu; Couillet, Romain; Mahoney, Michael W.
2021
When do neural networks outperform kernel methods? Zbl 07451719
Ghorbani, Behrooz; Mei, Song; Misiakiewicz, Theodor; Montanari, Andrea
2021
Understanding approximate Fisher information for fast convergence of natural gradient descent in wide neural networks. Zbl 07451720
Karakida, Ryo; Osawa, Kazuki
2021
Dual cruise-control limit cellular automaton model with cell length refinement in the framework of the three-phase traffic theory. Zbl 07430610
Li, Qi-Lang; Ye, Lin-Ling; Fu, Ding-Jun; Jiang, Rui; Wang, Bing-Hong
2021
Heavy-tailed distributions in a stochastic gene autoregulation model. Zbl 07430620
Bokes, Pavol
2021
Soliton gas in integrable dispersive hydrodynamics. Zbl 07430626
2021
$$T\overline{T}$$ deformation of the Ising model and its ultraviolet completion. Zbl 07430628
LeClair, André
2021
Anomalous thermal relaxation of Langevin particles in a piecewise-constant potential. Zbl 07430629
Walker, Matthew R.; Vucelja, Marija
2021
Good speciation and endogenous business cycles in a constraint satisfaction macroeconomic model. Zbl 07382821
Sharma, Dhruv; Bouchaud, Jean-Philippe; Tarzia, Marco; Zamponi, Francesco
2021
Correlations and structure of interfaces in the Ising model: theory and numerics. Zbl 07400668
Squarcini, Alessio; Tinti, Antonio
2021
Exponential corrected thermodynamics of black holes. Zbl 07399577
Pourhassan, Behnam
2021
Global multivariate model learning from hierarchically correlated data. Zbl 07399580
Horta, Edwin Rodríguez; Lage-Castellanos, Alejandro; Weigt, Martin; Barrat-Charlaix, Pierre
2021
Rule 54: exactly solvable model of nonequilibrium statistical mechanics. Zbl 07399583
Buča, Berislav; Klobas, Katja; Prosen, Tomaž
2021
On dissipative symplectic integration with applications to gradient-based optimization. Zbl 1489.82010
França, Guilherme; Jordan, Michael I.; Vidal, René
2021
When will an elevator arrive? Zbl 07398322
Feng, Zhijie; Redner, S.
2021
$$U_q(\mathfrak{sl}n)$$ web models and $$\mathbb{Z}_n$$ spin interfaces. Zbl 07398333
Lafay, Augustin; Gainutdinov, Azat M.; Jacobsen, Jesper Lykke
2021
The loss surfaces of neural networks with general activation functions. Zbl 07398345
2021
Wide neural networks of any depth evolve as linear models under gradient descent. Zbl 07330523
Lee, Jaehoon; Xiao, Lechao; Schoenholz, Samuel S.; Bahri, Yasaman; Novak, Roman; Sohl-Dickstein, Jascha; Pennington, Jeffrey
2020
Symmetry resolved entanglement entropy of excited states in a CFT. Zbl 1459.81097
Capizzi, Luca; Ruggiero, Paola; Calabrese, Pasquale
2020
A mean-field vaccination game scheme to analyze the effect of a single vaccination strategy on a two-strain epidemic spreading. Zbl 1456.92131
Arefin, Md Rajib; Kabir, K. M. Ariful; Tanimoto, Jun
2020
Scaling description of generalization with number of parameters in deep learning. Zbl 1459.82250
Geiger, Mario; Jacot, Arthur; Spigler, Stefano; Gabriel, Franck; Sagun, Levent; d’Ascoli, Stéphane; Biroli, Giulio; Hongler, Clément; Wyart, Matthieu
2020
Symmetry resolved entanglement in two-dimensional systems via dimensional reduction. Zbl 1459.81138
Murciano, Sara; Ruggiero, Paola; Calabrese, Pasquale
2020
Periodically driven jump processes conditioned on large deviations. Zbl 1456.60192
Chabane, Lydia; Chétrite, Raphaël; Verley, Gatien
2020
Symmetry resolved entanglement: exact results in 1D and beyond. Zbl 1456.81064
Fraenkel, Shachar; Goldstein, Moshe
2020
Large deviations for the Kardar-Parisi-Zhang equation from the Kadomtsev-Petviashvili equation. Zbl 1457.82362
Le Doussal, Pierre
2020
On entanglement Hamiltonians of an interval in massless harmonic chains. Zbl 1456.81324
Di Giulio, Giuseppe; Tonni, Erik
2020
Based on mathematical epidemiology and evolutionary game theory, which is more effective: quarantine or isolation policy? Zbl 1456.92128
Alam, Muntasir; Kabir, K. M. Ariful; Tanimoto, Jun
2020
Exact equivalences and phase discrepancies between random matrix ensembles. Zbl 1459.60014
Santilli, Leonardo; Tierz, Miguel
2020
Notes on matrix models (matrix musings). Zbl 1459.81094
Anninos, Dionysios; Mühlmann, Beatrix
2020
Entanglement Hamiltonians for non-critical quantum chains. Zbl 1459.81017
Eisler, Viktor; Di Giulio, Giuseppe; Tonni, Erik; Peschel, Ingo
2020
Conformal symplectic and relativistic optimization. Zbl 07330529
França, Guilherme; Sulam, Jeremias; Robinson, Daniel P.; Vidal, René
2020
The convex hull of the run-and-tumble particle in a plane. Zbl 1456.60105
Hartmann, Alexander K.; Majumdar, Satya N.; Schawe, Hendrik; Schehr, Grégory
2020
Uncovering the dynamics of correlation structures relative to the collective market motion. Zbl 1459.91223
Heckens, Anton J.; Krause, Sebastian M.; Guhr, Thomas
2020
Disentangling feature and lazy training in deep neural networks. Zbl 1459.68184
Geiger, Mario; Spigler, Stefano; Jacot, Arthur; Wyart, Matthieu
2020
Ultrametric fitting by gradient descent. Zbl 07330525
Chierchia, Giovanni; Perret, Benjamin
2020
Quantum thermalization and Virasoro symmetry. Zbl 1456.81352
Beşken, Mert; Datta, Shouvik; Kraus, Per
2020
The $$1 + 1$$ dimensional Kardar-Parisi-Zhang equation: more surprises. Zbl 1457.82292
Spohn, Herbert
2020
Aspects of the $$s$$ transformation bootstrap. Zbl 1456.81355
Brehm, Enrico M.; Das, Diptarka
2020
Entanglement Hamiltonian of the 1 + 1-dimensional free, compactified boson conformal field theory. Zbl 1459.81101
Roy, Ananda; Pollmann, Frank; Saleur, Hubert
2020
Run-and-tumble particle in inhomogeneous media in one dimension. Zbl 1459.60177
Singh, Prashant; Sabhapandit, Sanjib; Kundu, Anupam
2020
Entanglement revivals as a probe of scrambling in finite quantum systems. Zbl 1459.82074
Modak, Ranjan; Alba, Vincenzo; Calabrese, Pasquale
2020
Actions of the monodromy matrix elements onto $$\mathfrak{g}\mathfrak{l}\left(m\vert n\right)$$-invariant Bethe vectors. Zbl 1459.82069
Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.
2020
Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition. Zbl 1459.82313
Schrack, Lukas; Petersen, Charlotte F.; Jung, Gerhard; Caraglio, Michele; Franosch, Thomas
2020
Phase transition in complex-time Loschmidt echo of short and long range spin chain. Zbl 1457.82300
Santilli, Leonardo; Tierz, Miguel
2020
Wigner function of a quantum system with polynomial potential. Zbl 1456.81293
Perepelkin, E. E.; Sadovnikov, B. I.; Inozemtseva, N. G.; Burlakov, E. V.
2020
Driven tracers in a one-dimensional periodic hard-core lattice gas. Zbl 1456.60261
2020
Effective equations in complex systems: from Langevin to machine learning. Zbl 1459.82246
Vulpiani, Angelo; Baldovin, Marco
2020
The spectral dimension of simplicial complexes: a renormalization group theory. Zbl 1459.05356
Bianconi, Ginestra; Dorogovstev, Sergey N.
2020
Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example. Zbl 1459.82199
Wang, Shanshan; Gartzke, Sebastian; Schreckenberg, Michael; Guhr, Thomas
2020
Effect of local dissociations in bidirectional transport of driven particles. Zbl 1459.82284
Jindal, Akriti; Kolomeisky, Anatoly B.; Gupta, Arvind Kumar
2020
Intermittent resetting potentials. Zbl 1459.60165
Mercado-Vásquez, Gabriel; Boyer, Denis; Majumdar, Satya N.; Schehr, Grégory
2020
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup*. Zbl 07330531
Goldt, Sebastian; Advani, Madhu S.; Saxe, Andrew M.; Krzakala, Florent; Zdeborová, Lenka
2020
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### Cited by 5,808 Authors

 26 Calabrese, Pasquale 19 Takayanagi, Tadashi 18 Crampé, Nicolas 16 Doyon, Benjamin 16 Tonni, Erik 15 Myers, Robert C. 14 Majumdar, Satya N. 14 Monthus, Cécile 14 Slavnov, Nikita A. 13 Duan, Jinqiao 13 Ragoucy, Eric 13 Schehr, Grégory 13 Terwilliger, Paul M. 12 Nishioka, Tatsuma 12 Zinn-Justin, Paul 11 Casini, Horacio 11 Tanimoto, Jun 10 Ryu, Shinsei 9 Belliard, Samuel 9 de Gier, Jan 9 Doikou, Anastasia 9 Pronko, Andrei G. 9 Sierra, Germán 9 Vinet, Luc 8 Bajnok, Zoltán 8 Bueno, Pablo 8 Di Giulio, Giuseppe 8 Fu, Xinchu 8 Gaspard, Pierre 8 Gupta, Arvind Kumar 8 Hartman, Thomas E. 8 Kozlowski, Karol Kajetan 7 Ares, Filiberto 7 Baseilhac, Pascal 7 Bogolyubov, Nikolaĭ Mikhaĭlovich 7 Castro-Alvaredo, Olalla A. 7 Dong, Xi 7 Jack, Robert L. 7 Kundu, Anupam 7 Morin-Duchesne, Alexi 7 Mozaffar, M. Reza Mohammadi 7 Niccoli, Giuliano 7 Pakuliak, Stanislav Z. 7 Pearce, Paul A. 7 Pozsgay, Balázs 7 Song, Weiguo 7 Spagnolo, Bernardo 7 Valenti, Davide 7 Viti, Jacopo 7 Zhang, Jiaju 6 Alba, Vincenzo 6 Cardy, John L. 6 Chertkov, Michael 6 Cirac, Juan Ignacio 6 Colomo, Filippo 6 Cugliandolo, Leticia F. 6 De Bruyne, Benjamin 6 Ferrari, Patrik Lino 6 Fioravanti, Davide 6 Gradenigo, Giacomo 6 Großkinsky, Stefan 6 He, Song 6 Komatsu, Shota 6 Krapivsky, Pavel L. 6 Lecomte, Vivien 6 Lukyanov, Sergei L. 6 Mezzadri, Francesco 6 Motegi, Kohei 6 Nepomechie, Rafael I. 6 Nozaki, Masahiro 6 Parisi, Giorgio 6 Piroli, Lorenzo 6 Ricci-Tersenghi, Federico 6 Ridout, David 6 Rodríguez-Laguna, Javier 6 Ruggiero, Paola 6 Saleur, Hubert 6 Schütz, Gunter M. 6 Sun, Penggang 6 Vulpiani, Angelo 6 Wang, Wei 6 Watanabe, Kento 6 Yang, Wenli 6 Zeng, Chunhua 5 Bertoin, Jean 5 Bianchi, Lorenzo 5 Biroli, Giulio 5 Bouchaud, Jean-Philippe 5 Chen, Bin 5 Chernyak, Vladimir Y. 5 Derrida, Bernard 5 Di Francesco, Philippe 5 Evans, Martin R. 5 Faulkner, Thomas 5 Gombor, Tamás 5 Guhr, Thomas 5 Guseinov, D. V. 5 Iubini, Stefano 5 Jacobsen, Jesper Lykke 5 Jindal, Akriti ...and 5,708 more Authors
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### Cited in 332 Journals

 544 Journal of Statistical Mechanics: Theory and Experiment 463 Journal of High Energy Physics 288 Physica A 152 Journal of Statistical Physics 122 Nuclear Physics. B 106 Chaos, Solitons and Fractals 63 Communications in Mathematical Physics 55 Journal of Mathematical Physics 45 Journal of Physics A: Mathematical and Theoretical 41 Chaos 33 New Journal of Physics 33 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 32 Applied Mathematics and Computation 28 Communications in Nonlinear Science and Numerical Simulation 26 Physics Letters. B 23 Journal of Fluid Mechanics 23 Physics Reports 21 Letters in Mathematical Physics 21 Physica D 18 Electronic Journal of Probability 17 Physics Letters. A 16 The Annals of Probability 16 Annales Henri Poincaré 15 Theoretical and Mathematical Physics 15 Applied Mathematical Modelling 15 Fractals 15 Journal of Theoretical Biology 13 Journal of Computational Physics 13 Probability Theory and Related Fields 13 Mathematical Biosciences and Engineering 12 Neural Computation 12 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 12 SIAM Journal on Mathematics of Data Science 11 Classical and Quantum Gravity 11 Stochastic Processes and their Applications 11 Data Mining and Knowledge Discovery 10 Journal of Mathematical Biology 10 The Annals of Statistics 10 Information Sciences 10 Proceedings of the National Academy of Sciences of the United States of America 10 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 10 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 9 International Journal of Theoretical Physics 9 Journal of Combinatorial Theory. Series A 9 The Annals of Applied Probability 9 Journal of Mathematical Sciences (New York) 7 Advances in Mathematics 7 Mathematics and Computers in Simulation 7 Theoretical Population Biology 7 Linear Algebra and its Applications 7 SIAM Journal on Applied Mathematics 6 Computers & Mathematics with Applications 6 Bulletin of Mathematical Biology 6 Reviews in Mathematical Physics 6 Journal of Algebra 6 Transactions of the American Mathematical Society 6 Advances in Applied Mathematics 6 Physical Review Letters 6 Journal of Cosmology and Astroparticle Physics 5 Journal of the Franklin Institute 5 Computing 5 Theoretical Computer Science 5 European Journal of Operational Research 5 Discrete Dynamics in Nature and Society 5 SIAM Journal on Applied Dynamical Systems 5 Networks and Spatial Economics 5 Advances in High Energy Physics 4 Discrete Mathematics 4 General Relativity and Gravitation 4 Journal of Functional Analysis 4 Neural Networks 4 Machine Learning 4 Applied and Computational Harmonic Analysis 4 Bernoulli 4 Quantitative Finance 4 Discrete and Continuous Dynamical Systems. Series B 4 Journal of Systems Science and Complexity 4 Journal of Machine Learning Research (JMLR) 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 4 Statistical Analysis and Data Mining 4 Advances in Mathematical Physics 4 Computer Science Review 3 Advances in Applied Probability 3 Computers and Fluids 3 Computer Methods in Applied Mechanics and Engineering 3 Computer Physics Communications 3 Mathematical Biosciences 3 Applied Mathematics and Optimization 3 Journal of Applied Probability 3 Journal of Approximation Theory 3 Statistics & Probability Letters 3 Journal of Scientific Computing 3 Annals of Operations Research 3 Journal of Nonlinear Science 3 Theory of Probability and Mathematical Statistics 3 Computational and Applied Mathematics 3 Journal of Computational Neuroscience 3 Electronic Communications in Probability 3 Discrete and Continuous Dynamical Systems ...and 232 more Journals
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### Cited in 60 Fields

 1,393 Statistical mechanics, structure of matter (82-XX) 912 Quantum theory (81-XX) 428 Probability theory and stochastic processes (60-XX) 339 Relativity and gravitational theory (83-XX) 255 Combinatorics (05-XX) 240 Biology and other natural sciences (92-XX) 228 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 187 Computer science (68-XX) 171 Statistics (62-XX) 136 Partial differential equations (35-XX) 120 Operations research, mathematical programming (90-XX) 117 Dynamical systems and ergodic theory (37-XX) 113 Information and communication theory, circuits (94-XX) 100 Nonassociative rings and algebras (17-XX) 96 Fluid mechanics (76-XX) 80 Numerical analysis (65-XX) 79 Ordinary differential equations (34-XX) 67 Linear and multilinear algebra; matrix theory (15-XX) 52 Mechanics of particles and systems (70-XX) 46 Systems theory; control (93-XX) 43 Classical thermodynamics, heat transfer (80-XX) 38 Algebraic geometry (14-XX) 37 Associative rings and algebras (16-XX) 37 Special functions (33-XX) 31 Global analysis, analysis on manifolds (58-XX) 30 Differential geometry (53-XX) 24 Measure and integration (28-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 19 Functional analysis (46-XX) 19 Mechanics of deformable solids (74-XX) 17 Number theory (11-XX) 17 Operator theory (47-XX) 16 Optics, electromagnetic theory (78-XX) 14 Group theory and generalizations (20-XX) 14 Functions of a complex variable (30-XX) 13 Manifolds and cell complexes (57-XX) 13 Geophysics (86-XX) 10 Real functions (26-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 9 Difference and functional equations (39-XX) 9 Integral equations (45-XX) 6 Topological groups, Lie groups (22-XX) 6 Convex and discrete geometry (52-XX) 6 Algebraic topology (55-XX) 5 Geometry (51-XX) 5 Astronomy and astrophysics (85-XX) 4 History and biography (01-XX) 4 Category theory; homological algebra (18-XX) 4 Approximations and expansions (41-XX) 4 Integral transforms, operational calculus (44-XX) 3 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX)


text:
Outlook: Newpark Resources Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Hold
Time series to forecast n: 16 Mar 2023 for (n+1 year)
Methodology : Modular Neural Network (News Feed Sentiment Analysis)

## Abstract

Newpark Resources Inc. Common Stock prediction model is evaluated with Modular Neural Network (News Feed Sentiment Analysis) and Chi-Square1,2,3,4 and it is concluded that the NR stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Hold

## Key Points

1. Prediction Modeling
2. What is statistical models in machine learning?
3. Can machine learning predict?

## NR Target Price Prediction Modeling Methodology

We consider Newpark Resources Inc. Common Stock Decision Process with Modular Neural Network (News Feed Sentiment Analysis) where A is the set of discrete actions of NR stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Chi-Square)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (News Feed Sentiment Analysis)) X S(n):→ (n+1 year) $∑ i = 1 n s i$

n:Time series to forecast

p:Price signals of NR stock

j:Nash equilibria (Neural Network)

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## NR Stock Forecast (Buy or Sell) for (n+1 year)

Sample Set: Neural Network
Stock/Index: NR Newpark Resources Inc. Common Stock
Time series to forecast n: 16 Mar 2023 for (n+1 year)

According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Hold

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Grey to Black): *Technical Analysis%

## IFRS Reconciliation Adjustments for Newpark Resources Inc. Common Stock

1. An entity that first applies these amendments at the same time it first applies this Standard shall apply paragraphs 7.2.1–7.2.28 instead of paragraphs 7.2.31–7.2.34.
2. An entity shall apply Annual Improvements to IFRS Standards 2018–2020 to financial liabilities that are modified or exchanged on or after the beginning of the annual reporting period in which the entity first applies the amendment.
3. For example, Entity A, whose functional currency is its local currency, has a firm commitment to pay FC150,000 for advertising expenses in nine months' time and a firm commitment to sell finished goods for FC150,000 in 15 months' time. Entity A enters into a foreign currency derivative that settles in nine months' time under which it receives FC100 and pays CU70. Entity A has no other exposures to FC. Entity A does not manage foreign currency risk on a net basis. Hence, Entity A cannot apply hedge accounting for a hedging relationship between the foreign currency derivative and a net position of FC100 (consisting of FC150,000 of the firm purchase commitment—ie advertising services—and FC149,900 (of the FC150,000) of the firm sale commitment) for a nine-month period.
4. If an entity prepares interim financial reports in accordance with IAS 34 Interim Financial Reporting the entity need not apply the requirements in this Standard to interim periods prior to the date of initial application if it is impracticable (as defined in IAS 8).

*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.

## Conclusions

Newpark Resources Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Newpark Resources Inc. Common Stock prediction model is evaluated with Modular Neural Network (News Feed Sentiment Analysis) and Chi-Square1,2,3,4 and it is concluded that the NR stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Hold

### NR Newpark Resources Inc. Common Stock Financial Analysis*

Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBaa2Baa2
Balance SheetBaa2B1
Leverage RatiosCBaa2
Cash FlowBa3C
Rates of Return and ProfitabilityBaa2B1

*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?

### Prediction Confidence Score

Trust metric by Neural Network: 92 out of 100 with 873 signals.

## References

1. Bessler, D. A. T. Covey (1991), "Cointegration: Some results on U.S. cattle prices," Journal of Futures Markets, 11, 461–474.
2. P. Marbach. Simulated-Based Methods for Markov Decision Processes. PhD thesis, Massachusetts Institute of Technology, 1998
3. M. L. Littman. Markov games as a framework for multi-agent reinforcement learning. In Ma- chine Learning, Proceedings of the Eleventh International Conference, Rutgers University, New Brunswick, NJ, USA, July 10-13, 1994, pages 157–163, 1994
4. S. Bhatnagar, H. Prasad, and L. Prashanth. Stochastic recursive algorithms for optimization, volume 434. Springer, 2013
5. Keane MP. 2013. Panel data discrete choice models of consumer demand. In The Oxford Handbook of Panel Data, ed. BH Baltagi, pp. 54–102. Oxford, UK: Oxford Univ. Press
6. C. Wu and Y. Lin. Minimizing risk models in Markov decision processes with policies depending on target values. Journal of Mathematical Analysis and Applications, 231(1):47–67, 1999
7. Armstrong, J. S. M. C. Grohman (1972), "A comparative study of methods for long-range market forecasting," Management Science, 19, 211–221.
Frequently Asked QuestionsQ: What is the prediction methodology for NR stock?
A: NR stock prediction methodology: We evaluate the prediction models Modular Neural Network (News Feed Sentiment Analysis) and Chi-Square
Q: Is NR stock a buy or sell?
A: The dominant strategy among neural network is to Hold NR Stock.
Q: Is Newpark Resources Inc. Common Stock stock a good investment?
A: The consensus rating for Newpark Resources Inc. Common Stock is Hold and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of NR stock?
A: The consensus rating for NR is Hold.
Q: What is the prediction period for NR stock?
A: The prediction period for NR is (n+1 year)


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# zbMATH — the first resource for mathematics

On subalgebras of simple Lie algebras of characteristic $$p>0$$. (English) Zbl 0555.17003
This paper studies subalgebras of a simple finite-dimensional Lie algebra $$L$$ over an algebraically closed field of characteristic $$p\geq 7$$, especially subalgebras associated with filtrations.
The first main result implies that if a maximal subalgebra $$L_ 0$$ of $$L$$ has solvable quotients of dimension $$\geq 2$$, then every nilpotent ideal of $$L_0$$ acts nilpotently on $$L$$. It is shown that if $$L$$ contains a solvable maximal subalgebra, then $$L$$ is of type $$A_1$$ or $$W_1$$.
In the final part of the article it is shown that certain $$Z$$-graded finite- dimensional simple Lie algebras either are classical or the difference between the number of nonzero positive and negative homogeneous components is large.
Reviewer: Gordon Brown

##### MSC:
 17B50 Modular Lie (super)algebras 17B70 Graded Lie (super)algebras
Full Text:


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Find the maxium $\frac{bc}{a^{2}b+a^{2}c}+\frac{ac}{b^{2}a+b^2c}+\frac{ab}{c^2a+c^{2}b}$

1) $a, b, c$ are triangle edges's length such that $abc = 1$. Find max: $$\frac{bc}{a^{2}b+a^{2}c}+\frac{ac}{b^{2}a+b^2c}+\frac{ab}{c^2a+c^{2}b}$$

My idea: $$\frac{bc}{a^{2}b+a^{2}c}+\frac{ac}{b^{2}a+b^2c}+\frac{ab}{c^2a+c^{2}b}=\frac{abc}{a^3(b+c)}+\frac{abc}{b^{3}(c+a)}+\frac{abc}{c^3(a+b)}$$ Then use AM-GM ? I just can find min: $$\frac{1}{a^{3}\left ( b+c \right )}+\frac{1}{b^{3}\left ( c+a \right )}+\frac{1}{c^{3}\left ( a+b \right )}\geq \frac{3}{2}$$

2) Find for $x$, $y$, $z$ such that $\left\{\begin{matrix} xy + 2(x+y)=0\\ \ yz + 2(y+z)=-3\\ zx + 2(z+x)=5 \end{matrix}\right.$

(Some one should edit my post: correct grammar...)

-
two unrelated questions in one. why don't you separate them. –  user31280 Nov 23 '12 at 11:32
I think we can't find max of $$\frac{bc}{a^{2}b+a^{2}c}+\frac{ac}{b^{2}a+b^2c}+\frac{ab}{c^2a+c^{2}b}$$ –  D3r0X4 Nov 23 '12 at 12:47

Hint: For your second question, subtracting the equations in pairs suggests the substitution $$a=x+2,\quad b=y+2, \quad c=z+2.$$ Try this in the original set of equations.
For $0 < \epsilon < 1$ and $a = \epsilon^2$, $b = c = \frac 1 \epsilon$ we have $$abc = 1\\ a = \epsilon^2 \leq \frac 2 \epsilon = b + c \\ b = \frac 1 \epsilon \leq \frac 1 \epsilon + \epsilon^2 = a + c \\ c = \frac 1 \epsilon \leq \frac 1 \epsilon + \epsilon^2 = a + b$$ All question conditions are satisfied.
Now $$I := \frac{bc}{a^{2}b+a^{2}c}+\frac{ac}{b^{2}a+b^2c}+\frac{ab}{c^2a+c^{2}b} \geq \frac{bc}{a^{2}b+a^{2}c} = \frac 1 {a^3(b +c)} = \frac 1 {2\epsilon^5}$$ so for arbitrarily small $\epsilon$ we get arbitrarily great $I$.


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# There is one point I don't understand about G-torsor.

1. Jul 14, 2007

### kakarukeys

There is one point I don't understand about G-torsor.

A Lie group G acts freely and transitively on a manifold F.
F x G -> F
(f, g) -> fg, f(g1g2) = (fg1)g2
is a smooth map.

fix an element f of F
then the map h
F -> G
fg -> g
is a homeomorphism.

I know h is open from the continuity of the map
{f} x G -> F
g -> fg

How to see h is continuous?

Last edited: Jul 14, 2007
2. Jul 20, 2007

### kakarukeys

please help!!!!! I'm desperate. I will help out in the Homework and coursework questions section if anybody can help me.

3. Aug 2, 2007

### LorenzoMath

Your description of the map h: F -> G seems to have a typo. I guess you meant it to be f -> fg.

h is factored through Stab(g), right? Now Stab(g) is trivial and h is surjective since F is a G-torsor. Thus h is one-to-one.

By definition h is continuous, so h is bijective and continuous. Since in addition F and G are locally compact and Hausdorff, h is a homeomorphism.

4. Aug 6, 2007

### kakarukeys

No, there is no typo, I have typed a little too fast. Let me use Latex and state my question clearer.

There is one point I don't understand about G-torsor.

A Lie group G acts freely and transitively on a manifold F.
$$\rho: F \times G \longrightarrow F$$
$$\rho(f, g) = fg$$
$$f(g_1g_2) = (fg_1)g_2$$

fix an element f of F
then the map
$$h_f: \{fg | \forall g\in G\} \longrightarrow G$$
$$h_f(fg) = g$$
is a homeomorphism.

I know $$h_f$$ is open from the continuity of the map
$$\rho_f = h_f^{-1}$$
$$\rho_f: \{f\} \times G \longrightarrow F$$
$$\rho_f(g) = fg$$

How to see h is continuous?

Your h is my $$\rho_f$$. Were you saying $$\rho_f$$ is open because F, G are (required to be) locally compact and Hausdorff?

5. Aug 31, 2007

### kakarukeys

I couldn't find any theorem which guarantees that.

closests two are:

(1) if G is compact and F is Hausdorff, $$\rho_f$$ is open
(2) if G is locally compact, F is locally compact and Hausdorff, F is a topological group under the induced group operations, $$\rho_f$$ is open


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# Synopsis: Perhaps no “bump” in the data

Potential signs of new physics in an earlier particle collision experiment are now being questioned in a report from Fermilab.

An unexpected finding in a particle physics experiment must be reproduced to rule out the possibility that it is only a statistical fluctuation or due to something other than new physics.  This is a primary reason for having more than one experiment studying the same kind of signal at a high-energy particle collider.  At Fermilab, there are two such experiments: CDF and D0.

In April 2011, the CDF collaboration reported a $3.2$ standard deviation excess in the number of events with a $W$ boson and a pair of jets whose invariant mass was in the $120$$160$ giga-electron-volt ($\text{GeV}$) range (see T. Aaltonen et al., Phys. Rev. Lett. 106, 171801). One possible explanation for that excess was an unexpected new particle, with a cross section of approximately $4$ picobarn ($\text{pb}$). Now, the D0 collaboration reports in Physical Review Letters their analysis of the same type of events. They see no evidence for such an excess, ruling out a particle with a $4\phantom{\rule{0.333em}{0ex}}\text{pb}$ cross section at the $4.3$ standard deviation level.

The two Fermilab experiments appear to disagree, but it’s not yet clear why. To facilitate comparison between the results, D0 made their search parallel to the CDF search to a good approximation, but there were small differences in how the two collaborations handled systematic errors, and of course the detectors are different.

It is also possible that CDF saw an upward fluctuation in the production of some new particle while D0 saw a downward fluctuation. D0 addresses this possibility, showing their $p$ values for a range of potential signal cross sections. For example, there is only a $2%$ chance that a particle with a $2\phantom{\rule{0.333em}{0ex}}\text{pb}$ cross section is compatible with D0’s data.  Further results are needed to clarify the situation. – Robert Garisto

More Features »

### Announcements

More Announcements »

## Subject Areas

Particles and Fields

Nuclear Physics

## Next Synopsis

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text:
# AoMath: Slope Of Tangent Lines To Curves

Slope of the tangent line. Pretty odd thing to study you might say. Let's start by drawing a continous and curvey function in the Cartesian plane from (1, 1) to (4, 2). Look to see if there are any "hills and valleys." Notice that the slope of the tangent line at the very bottom and very top is ZERO! So:

1. We could find a function that tells us the slope at every x-value.
2. We could set it equal to zero to see which x-values have a slope of zero.
3. We could then use those x-values to help us find the tallest hill or the lowest valley.
But we have a ways to go before we can do all that.
So how do we find the slope of a tangent line, say at x = 1/2, of $$f(x) = 1 - x^2$$? First, we need a point on the graph at which we want to know the slope.

1. We find the point (c, f(c)) or (1/2, 3/4).
2. We draw the secant slope between the point above and any OTHER point on the function, in our case $$(x_0, f(x_0))$$.
3. We draw more and more secant lines but move that second point closer to (1/2, 3/4) until we are VERY CLOSE but NOT EQUAL TO the original point. Sounds like a limit! $$f'(c) = \lim_{x_0 \rightarrow c} \frac{f(x_0) - f(c)}{x_0 - c} = ??$$ $$\lim_{x_0 \rightarrow \frac{1}{2}} \frac{f(x_0) - f(\frac{1}{2})}{x_0 - \frac{1}{2}}$$ $$= \lim_{x_0 \rightarrow \frac{1}{2}} \frac{(1 - (x_0)^2) - (1 - (\frac{1}{2})^2)}{x_0 - \frac{1}{2}}$$ $$= \lim_{x_0 \rightarrow \frac{1}{2}} \frac{(\frac{1}{4} - (x_0)^2)}{x_0 - \frac{1}{2}}$$ $$= \lim_{x_0 \rightarrow \frac{1}{2}} \frac{(1 - 4(x_0)^2)}{4x_0 - 2}$$ $$= \lim_{x_0 \rightarrow \frac{1}{2}} \frac{(1 - 2(x_0))(1 + 2(x_0))}{2(2x_0 - 1)}$$ $$= \lim_{x_0 \rightarrow \frac{1}{2}} \frac{-(1 + 2(x_0))}{2} = \boxed{-1}$$


text:
Towards the beginning of the summer, I wrote up a post on how I think we could teach programs to program. The gist is that there’s a small-ish well typed program space worth exploring in pure functional programming. Pure strongly typed FP can be really restrictive in what programs it allows, which means a machine has fewer bad programs it has to try out.

I worked on it for a few months, but abandoned it around June or July. The next steps to improving it were big ones and, because it’s just a fun side project, they’re too big to be worthwhile. As such, I’m putting it on hold. That said, I learned a ton that might be worth sharing and wrote code people might be interested in, so here’s a little writeup. Maybe I’ll add more later, but don’t hold your breath.

The first steps I took were purely proof of concept. Can a neural network using basic RL learn to choose between alternative programs for this kind of problem? I set out to test this with a series of toy problems.

The first test was to learn whether a bunch of numbers were summed or multiplied. Given a list of pairs $(x_{1i}, x_{2i})$ and associated $y_i = x_{1i} \oplus x_{2i}$ where $\oplus$ is either addition or multiplication, I wanted to see whether a simple policy gradient algorithm could learn which gives smaller errors? I did this with policies that chose addition with probability $sigmoid(\theta)$ and multiplication otherwise, searching for a policy that minimized the error.

The most basic way to do policy gradient is to notice that $\nabla_\theta \mathbb{E}_X[f(x)] = \mathbb{E}_X[f(x) \nabla_\theta \textrm{ln}p(x)]$. This does ok, but the finite sample analogue is kinda crappy. Realizing that the gradients should be the same if we subtract some baseline $\nabla_\theta \mathbb{E}_X[f(x) - b]$, we can surprisingly decrease the variance of our gradient estimates by choosing a non-zero baseline. Simply setting the baseline to be $\mathbb{E}_X[f(x)]$, leading to gradient estimates of $\mathbb{E}_X[\{f(x) - \mathbb{E}_X[f(x)]\} \nabla_\theta \textrm{ln}p(x)]$ does a much better job.

Simple gradient descent on $\theta$ chooses the correct branch pretty much immediately.

# Addition or multiplication by what?

The next test was a little harder. This time it had to learn $y_i = x_i \oplus k$ for unknown operation $\oplus$ and constant $k$.

This one was harder. Schulman et al explain really well in their stochastic computation graph paper that a sampling step really just screws your gradients. This is tough when you have continuous parameters that the loss function should be cleanly differentiable with respect to. To make it fit into this kind of framework, I had to be able to sample $k$, so I chose to model it as a normal distribution with unknown mean and log variance. It would have been easier to use a different parameter for $k$ per branch of the $\oplus$ choice, cutting out the difficulties around sampling, but the whole point was to do a proof of concept on learning shared global weights in the simplest model.

The results were really interesting. Once I switched from the most basic policy gradient algorithm to the one with a baseline, it was able to learn the model pretty well most of the time, but not always. For one thing, the variance parameter decreased way too fast. If I forced it to stay artificially high, it would find the true value far more reliably, and allow the $\oplus$ time to find the right value as well, but it wouldn’t learn $k$ nearly as precisely. It was also pretty sensitive to parameter initialization.

With some tuning, it could learn quickly and precisely, so I moved on to a harder problem.

# Simply typed lambda calculus

Yay! The problem I wanted to do from the beginning! I treated it as a tree to sample from, with a stateful search recursing through the tree with an LSTM. Given an input variable x of type a and output variable y of type b, we can construct a candidate y by applying a lambda of type a -> b to x. This passes the buck up a step. What lambda should we construct?

Well, a lambda has two fields in it. The first is a variable (in this case a variable of type a), and the second is an expression of type b (with the new variable in scope). Each of these fields is is constructed recursively:

Each language rule can construct something, like an expression, variable, or primitive value of a given type. Many of the rules also have fields, like the a lambda’s variable and body fields.

The rules are also assigned embeddings. When trying to sample a field for a given rule, we need to give it a probability. We can construct unnormalized probabilities with some function $rule\_prob(state, rule\_embedding)$. We then sample from the valid rules that could make an expression of the desired type. We use that rule to make an expression/variable/primitive, constructing its own fields recursively, if it has any Eventually, the fields chosen are variables or primitives, which don’t have fields of their own.

For each field, we modify the state as a function of the rule that was chosen: $new\_state = state\_update(state, rule\_embedding)$. This lets the state represent the parts of the AST that have been created so far, and helps the model intelligently choose the rest of the AST.

In the end, we end up with an AST of the correct type, and a differentiable probability of that AST with respect to our model parameters.

We then apply the function $f$ from our AST to each $x_i$ and evaluate it, from which we can construct a not-necessarily-differentiable loss function $loss(f(x_i), y_i)$ and it’s probability. Applying reinforcement learning, we can find the parameters that make the true AST most likely to be generated.

If we sampled enough ASTs, we ought to be able to find the right one, and increase its probability, or at least increase the probabilities of better approximations to the true one. That’s a rough description, and the actual code is here. The lambda calculus I built for it to learn basically followed the one laid out in the Type Systems section of Stephen Diehl’s Write You a Haskell, plus a few more primitives.

It turns out that in the space of all ASTs in a simple language, most of them are huge, in the same way that most positive integers are over a million. Who would have thought!? At first, I thought I had a bug when I couldn’t generate a single AST, but then I realized it just took forever. Penalizing samples that overflowed some small depth, it was able to run quickly enough.

# Finally, results!

It didn’t take too horribly long to learn simple functions like lambda x: True, lambda (x1, x2): x1, or lambda (x1, x2): (x1 * x1) + x2 or other “programs” of similar complexity, but this is where I realized I was going down the wrong path. First of all, it took longer than I’d like to go from most most samples overflowing the maximum tree depth, to most samples being small enough to evaluate. Second, it took a huge number of iterations between first seeing the best AST and making it the most probably AST. In between, it would sample the same trees thousands of times with the same loss but different probabilities. Finally, with finite samples, it was really easy to get stuck in local minima, never seeing function the model ought to make more likely.

# Ouch

The simplest change would be to stop sampling from the possible trees and instead turn it into a search problem where we only see each possible tree at most once per gradient step. Importance sampling (or something like 12.5 of Koller and Friedman) might not be the right idea, but they seem like the right flavor. I don’t actually need an unbiased estimate of the gradient. All I really need is a way to intelligently decide where to search next in the tree of all possible ASTs. Gradients of stochastic policies seem like total overkill in retrospect.

The problem there is that I’d have to write this whole thing as an infinite tree of trees to explore, and that just seem like a pain in the butt.

Alternatively, moving to imperative-land could be promising. Given a list of variables $x_i$ in scope, try to turn each into $y_i$ by continuously manipulating them (in parallel) until they seem correct. All operations would have to happen uniformly across all $i$, so it couldn’t cheat much worse than just returning $mean(y)$ as a constant for all $i$. This “hack at it until it works” approach helps me think through new problems sometimes, so maybe it’s a decent attempt. It strikes me as an easier problem in a larger solution space, so who knows if it’ll be easier for a machine to find. ¯\_(ツ)_/¯

But both of those are too much work for a side project, so this is on hold for a while. :(

# What I learned

My takeaway from this whole project was that, when searching through huge/infinite spaces, an approach that samples individual points redundantly is a waste. Maximizing likelihood that good solutions are found doesn’t require that we start the search all over for every parameter update. The focus shouldn’t be on maximizing the likelihood of those points given that they are found, the focus should be on finding them in the first place.


text:
Four point charges form a square with sides of length , as shown in the figure. In the questions thatfollow, use the constant in place of .

(Intro1 figure)

PartA
What is the electric potential at the center of the square?

Make the usual assumption that the potential tends to zero faraway from a charge.

 =

PartB
What is the contribution to the electric potentialenergy of the system, due to interactions involving thecharge ?


text:
• # question_answer Which of the following is important in water cycle? A)  Transpiration through leaves B)  Evaporation from ocean C)  Percolation of water into the ground D)  Absorption of capillary water by plants

[b] The water cycle, also known as the hydrologic cycle or ${{H}_{2}}O$ cycle, describes the continuous movement of water on, above and below the surface of the Earth. Water can change states among liquid, vapour, and solid at various places in the water cycle. Although the balance of water on Earth remains fairly constant over time, individual water molecules can come and go, in and out of the atmosphere. The water moves from one reservoir to another, such as from river to ocean, or from the ocean to the atmosphere, by the physical processes of evaporation, condensation, precipitation, infiltration, runoff, and subsurface flow. In so doing, the water goes through different phases: liquid, solid, and gas.


text:
## Mathematical Society of Japan Memoirs

### Chapter 3. Projective representations and spin characters of complex reflection groups $G(m,p,n)$ and $G(m,p,\infty)$, II: Case of generalized symmetric groups

#### Abstract

In this paper we study projective (or spin) irreducible representations and their characters of generalized symmetric groups $G(m,1,n)$, and spin characters of their inductive limit groups $G(m,1,\infty)=\lim_{n\to\infty}G(m,1,n)$. The groups $G(m,1,n)$ form a subcategory of complex reflection groups $G(m,p,n),\,p|m$, and the present study has a fundamental importance for such studies for general $G(m,p,n)$'s. Schur multipliers $Z=H^2\big(G(m,1,n),\boldsymbol{C}^\times\big)$ are isomorphic to $\boldsymbol{Z}_2^{\;3}=\prod_{1\le i\le 3}\langle z_i\rangle,\, z_i^{\,2}=e,$ for $n\ge 4$ and $m\ge 2$ even, and similarly for $n=\infty$. Here, according to the semidirect product structure $G(m,1,n)=D_n\rtimes\mathfrak{S}_n$ with $D_n=\boldsymbol{Z}_m^{\;n}$, $z_1$ corresponds to the double covering group $\widetilde{\mathfrak{S}}_n$ of $\mathfrak{S}_n$, and $z_2$ to the double covering $\widetilde{D}_n$ of $D_n$, and $z_3$ to the twisted action of $\widetilde{\mathfrak{S}}_n$ on $\widetilde{D}_n$. In this case, any such representations and such characters have their own central characters $\chi\in\widehat{Z}$ with $(\beta_1,\beta_2,\beta_3),\,\beta_i=\chi(z_i)=\pm 1$, called (spin) type. Our study here is for two types $(-1,-1,-1)$ and $(-1,-1,\;1)$, and gives (1) classification and construction of all spin irreducible representations of $G(m,1,n)$, (2) calculation of their characters, (3) calculation of limits of normalized irreducible characters as $n\to \infty$, and (4) explicit determination of all the spin characters of $G(m,1,\infty)$ of these types.

#### Chapter information

Source
Takeshi Hirai, Akihito Hora, Etsuko Hirai, Projective Representations and Spin Characters of Complex Reflection Groups $G(m,p,n)$ and $G(m,p,\infty)$ (Tokyo: The Mathematical Society of Japan, 2013), 123-272

Dates
First available in Project Euclid: 13 October 2014

Hirai, Takeshi; Hora, Akihito; Hirai, Etsuko. Chapter 3. Projective representations and spin characters of complex reflection groups $G(m,p,n)$ and $G(m,p,\infty)$, II: Case of generalized symmetric groups. Projective Representations and Spin Characters of Complex Reflection Groups $G(m,p,n)$ and $G(m,p,\infty)$, 123--272, The Mathematical Society of Japan, Tokyo, Japan, 2013. doi:10.2969/msjmemoirs/02901C030. https://projecteuclid.org/euclid.msjm/1413220877


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# 50146. Merge Link Lists, Again

## I'm a slow walker, but I never walk backwards.

Write a program to merge several link lists into a single one. You are given the starting address of $K$ linked lists that are indexed from 0 to $K-1$. You will take $N$ iteration to merge the lists where $N$ is the length of the longest list.

You need to merge lists just like in the previous task when the flag ZIGZAG is set. In the first iteration, we link the first nodes (if they exist) from all lists in increasing index order. Please refer to the following figure for an illustration. In the second iteration we link the second nodes (if they exist) from all lists in decreasing index order, and put them after the list we constructed from the first iteration. The third iteration is just like the first iteration, and so on. Note that if a list does not have a node in an iteration, it is simply skipped in the construction. There will be $N$ iterations since there the length of the longest list is $N$. Finally we will get only one list.

example

Now we describe how to merge lists when the flag TOPDOWN is set. In every iteration we always link the nodes (if they exist) from all lists in increasing index order. Please refer to the following figure for an illustration.

example

Now we describe how to merge lists when the flag BOTTOMUP is set. In every iteration we always link the nodes (if they exist) from all lists in decreasing index order. Please refer to the following figure for an illustration.

example

The linked list node and the function you need to implement is defined in merge.h.

#ifndef MERGE_H#define MERGE_Htypedef struct node {    int data;    struct node *next;}Node;Node *merge(Node *list[], int K);#endif

You may use the following main function to test your function.

#include <stdio.h>#include <stdlib.h>#include "merge.h" int main () {        int K;        scanf("%d", &K);        Node *list[K];        for (int i = 0; i < K; i++) {                int N;                scanf("%d", &N);                if (N == 0) {                        list[i] = NULL;                        continue;                }                list[i] = (Node *)malloc(sizeof(Node));                scanf("%d", &(list[i]->data));                list[i]->next = NULL;                Node *previous = list[i];                for (int j = 1; j < N; j++) {                        previous->next = (Node *)malloc(sizeof(Node));                        scanf("%d", &(previous->next->data));                        previous->next->next = NULL;                        previous = previous->next;                }        }        Node *result = merge(list, K);        while (result) {                printf("%d", result->data);                result = result->next;                printf("%c", result ? ' ' : '\n');        };        return 0;}

## Compile

gcc -O2 -DZIGZAG main.c merge.c -o zigzaggcc -O2 -DTOPDOWN main.c merge.c -o topdowngcc -O2 -DBOTTOMUP main.c merge.c -o bottomup

## Input Format

The input contains only one test case. The first line contains $K$, the number of linked lists you need to merge. In the following $K$ lines, the first integer $N$ is the number of nodes in that list and the following $N$ integers are the values of nodes in that list.

## Output Format

Visit the merged linked list and print the value of each node in one line.

• 40 points: The flag ZIGZAG is set.
• 30 points: The flag TOPDOWN is set.
• 30 points: The flag BOTTOMUP is set.

## Sample Input 1

Compile with gcc -std=c99 -O2 -DZIGZAG main.c merge.c -o zigzag.

42 2 75 0 1 9 12 102 1 23 8 1 10

## Sample Output 1

2 0 1 8 1 2 1 7 9 10 12 10

## Sample Input 2

Compile with gcc -std=c99 -O2 -DTOPDOWN main.c merge.c -o topdown.

42 2 75 0 1 9 12 102 1 23 8 1 10

## Sample Output 2

2 0 1 8 7 1 2 1 9 10 12 10

## Sample Input 3

Compile with gcc -std=c99 -O2 -DBOTTOMUP main.c merge.c -o bottomup.

42 2 75 0 1 9 12 102 1 23 8 1 10

## Sample Output 3

8 1 0 2 1 2 1 7 10 9 12 10


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de.mpg.escidoc.pubman.appbase.FacesBean
English

# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Nuclear Level Densities at High Excitation Energies and for Large Particle Numbers

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons30873

Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons31164

Weidenmüller,  Hans A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

##### Fulltext (public)

1307.0400.pdf
(Preprint), 434KB

##### Supplementary Material (public)
There is no public supplementary material available
##### Citation

Pálffy, A., & Weidenmüller, H. A. (2013). Nuclear Level Densities at High Excitation Energies and for Large Particle Numbers. Nuclear Physics A, 917, 15-42. doi:10.1016/j.nuclphysa.2013.08.011.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6401-1
##### Abstract
Starting from an independent-particle model with a finite and arbitrary set of single-particle energies, we develop an analytical approximation to the many-body level density $\rho_A(E)$ and to particle-hole densities. We use exact expressions for the low-order moments and cumulants to derive approximate expressions for the coefficients of an expansion of these densities in terms of orthogonal polynomials. The approach is asymptotically (mass number $A \gg 1$) convergent and, for large $A$, covers about 20 orders of magnitude near the maximum of $\rho_A(E)$ (i.e., about half the spectrum). Densities of accessible states are calculated using the Fermi-gas model.


text:
Prealgebra (7th Edition)

$-12+10\div(-5)$ $\longrightarrow$ division is before addition in the order of operations =$-12+(-2)$ =$-14$


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## Speed of convergence to equilibrium in Wasserstein metrics for Kac's like kinetic equations    [PDF]

Federico Bassetti, Eleonora Perversi
This work deals with a class of one-dimensional measure-valued kinetic equations, which constitute extensions of the Kac caricature. It is known that if the initial datum belongs to the domain of normal attraction of an \alpha-stable law, the solution of the equation converges weakly to a suitable scale mixture of centered \alpha-stable laws. In this paper we present explicit exponential rates for the convergence to equilibrium in Kantorovich-Wasserstein distances of order p>\alpha, under the natural assumption that the distance between the initial datum and the limit distribution is finite. For \alpha=2 this assumption reduces to the finiteness of the absolute moment of order p of the initial datum. On the contrary, when \alpha<2, the situation is more problematic due to the fact that both the limit distribution and the initial datum have infinite absolute moment of any order p >\alpha. For this case, we provide sufficient conditions for the finiteness of the Kantorovich-Wasserstein distance.
View original: http://arxiv.org/abs/1205.3690


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Vectors with constants

1. Sep 10, 2011

renncat2

Let a$\vec{A}$+ b$\vec{B}$ + $\vec{C}$ = 0, where $\vec{A}$ = (75, -60), $\vec{B}$ = (-16, 60), and $\vec{C}$ = (84,16). I need to find the value of a and b. I really have no idea where to start with this problem any help would be great!

2. Sep 10, 2011

Hootenanny

Staff Emeritus
Welcome to Physics Forums.

You have two equations, with two unknowns. How do you suppose you could solve them?

3. Sep 10, 2011

renncat2

So far I found the magnitude of the resultant displacement. (Rx = 144, Ry = 16, $\vec{R}$ = 144.886)

4. Sep 10, 2011

Hootenanny

Staff Emeritus
The magnitude of the resultant vector is zero, by definition.

How do you normally solve systems of simultaneous equations?

5. Sep 10, 2011

renncat2

i don't know. can you give me an example?


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# Editor¶

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note:

If you select some text with the mouse and use the Ctrl + f shortcut, then:

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Note

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It will flow through the search terms history but not wrap around, simply end at the other end.

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