text:
# zbMATH — the first resource for mathematics

Harmonic analysis, cohomology, and the large-scale geometry of amenable groups. (English) Zbl 1064.43004
This paper explores aspects of geometric group theory involving representation theory and cohomology. Two groups $$\Gamma$$ and $$\Lambda$$ generated by finite symmetric sets are called quasi-isomorphic if there is a map $$\phi$$ from $$\Lambda$$ to $$\Gamma$$ and constants $$\alpha\geq 1$$ and $$K\geq 0$$ such that for all $$\lambda_1$$, $$\lambda_2$$ in $$\Lambda$$ $\alpha^{-1} d_\Lambda(\lambda_1, \lambda_2)- K\leq d_\Gamma(\phi\lambda_1, \phi\lambda_2)\leq \alpha d_\Lambda(\lambda_1, \lambda_2)+ K$ and any element of $$\Lambda$$ is within distance $$\leq K$$ from $$\phi\Lambda$$. Here $$d_\Lambda$$ and $$d_\Gamma$$ are the word metrics on the respective groups. The author explores various implications of quasi-isometry to a host of settings.
The first result is that if $$\Gamma$$ is quasi-isomorphic to $$\mathbb{Z}^d$$, then $$\Gamma$$ has a finite index subgroup isomorphic to $$\mathbb{Z}^d$$. Other results that bring in cohomology for quasi-isomorphic groups are as follows: If $$\Gamma$$ and $$\Lambda$$ are finitely generated, then all of their respective Betti numbers are equal. If $$\Gamma$$ is quasi-isomorphic to a polycyclic group, then all of its virtual Betti numbers are greater than zero. The cohomological dimensions of $$\Gamma$$ and $$\Lambda$$ over a ring $$R$$ are identical. The author also applies his techniques to a class of non-finitely presentable abelian-by-cyclic groups.
The author discusses a notion more general than quasi-isometry, namely, uniform embedding. Many of the results for quasi-isomorphic groups hold for uniformly embedded pairs of groups. For example, cohomological dimensions are preserved. Having the type (FP) property and for solvable groups $$\Gamma$$ and $$\Lambda$$, the Hirsh number of $$\Lambda$$ is bounded by that of $$\Gamma$$.
Let $$\Gamma$$ be a discrete group. Definition: $$\Gamma$$ has property $$H_{FD}$$ if for every unitary representation $$\pi$$ of $$\Gamma$$ with non-zero first cohomology with respect to $$\pi$$ there exists a finite-dimensional $$\Gamma$$-subrepresentation. The author proves that among amenable groups, the property $$H_{FD}$$ is a quasi-isometry invariant.

##### MSC:
 43A07 Means on groups, semigroups, etc.; amenable groups 43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 20J06 Cohomology of groups
Full Text:
##### References:
 [1] Assouad, P., Plongements lipschitziens dansR n .Bull. Soc. Math. France, 111 (1983), 429–448. · Zbl 0597.54015 [2] Baumslag, G., Wreath products and finitely presented groups.Math. Z., 75 (1960/1961). 22–28. · Zbl 0090.24402 [3] Benjamini, I. &Schramm, O., Every graph with a positive Cheeger constant contains a tree with a positive Cheeger constant.Geom. Funct. Anal., 7 (1997), 403–419. · Zbl 0882.05052 [4] Benoist, Y., Private communication (available upon request). [5] Bergelson, V., Weakly mixing PET.Ergodic Theory Dynam Systems, 7 (1987), 337–349. · Zbl 0645.28012 [6] Bergelson, V. &Rosenblatt, J., Mixing actions of groups.Illinois J. Math., 32 (1988), 65–80. · Zbl 0619.43005 [7] Bestvina, M. &Feighin, M., Proper actions of lattices on contractible manifolds.Invent. Math., 150 (2002), 237–256. · Zbl 1041.57015 [8] Bestvina, M., Kapovich, M. &Kleiner, B., van Kampen’s embedding obstruction for discrete groups.Invent. Math., 150 (2002), 219–235. · Zbl 1041.57016 [9] Bieri, R.,Homological Dimensibn of Discrete Groups. Queen Mary College Mathematics Notes, Queen Mary College, London, 1976. · Zbl 0357.20027 [10] Bieri, R. &Strebel, R., Almost finitely presented soluble groups.Comment. Math. Helv., 53 (1978), 258–278. · Zbl 0373.20035 [11] Block, J. &Weinberger, S., Large scale homology theories and geometry, inGeometric Topology (Athens, GA, 1993), pp. 522–569. AMS/IP Stud. Adv. Math., 2.1., Amer. Math. Soc., Providence, RI, 1997. · Zbl 0898.55006 [12] Borel, A. &Serre, J.-P., Corners and arithmetic groups.Comment. Math. Helv., 48 (1973), 436–491. · Zbl 0274.22011 [13] Bourdon, M. &Pajot, H., Rigidity of quasi-isometries for some hyperbolic buildings.Comment. Math. Helv., 75 (2000), 701–736. · Zbl 0976.30011 [14] Bridson, M. R. &Gersten, S. M., The optimal isoperimetric inequality for torus bundles over the circle.Q. J. Math., 47 (1996), 1–23. · Zbl 0852.20031 [15] Chou, C., Elementary amenable groups.Illinois J. Math., 24 (1980), 396–407. · Zbl 0439.20017 [16] Delorme, P., 1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations.Bull. Soc. Math. France, 105 (1977), 281–336. · Zbl 0404.22006 [17] Drutu, C., Quasi-isometry invariants and asymptotic cones.Internat. J. Algebra Comput., 12 (2002), 99–135. · Zbl 1010.20029 [18] Dunwoody, M. J., Accessibility and groups of cohomological dimension one.Proc. London Math. Soc., 38 (1979), 193–215. · Zbl 0419.20040 [19] Dyubina, A., Instability of the virtual solvability and the property of being virtually torsion-free for quasi-isometric groups.Int. Math. Res. Not., 2000 (2000), 1997–1101. · Zbl 0979.20034 [20] Erschler, A., On isoperimetric profiles of finitely generated groups.Geom. Dedicata, 100 (2003), 151–171. · Zbl 1049.20024 [21] Farb, B., The quasi-isometry classification of lattices in semisimple Lie groups.Math. Res. Lett., 4 (1997), 705–717. · Zbl 0889.22010 [22] Farb, B. &Mosher, L., A rigidity theorem for the solvable Baumslag-Solitar groups.Invent. Math., 131 (1998), 419–451. · Zbl 0937.22003 [23] –, Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II.Invent. Math., 137 (1999), 613–649. · Zbl 0931.20035 [24] –, On the asymptotic geometry of abelian-by-cyclic groups.Acta Math., 184 (2000), 145–202. · Zbl 0982.20026 [25] –, Problems on the geometry of finitely generated solvable groups, inCrystallographic Groups and their Generalizations (Kortrijk, 1999), pp. 121–134. Contemp. Math., 262. Amer. Math. Soc., Providence, RI, 2000. [26] –, The geometry of surface-by-free groups.Geom. Funct. Anal., 12 (2002), 915–963. · Zbl 1048.20026 [27] Gersten, S. M., Quasi-isometry invariance of cohomological dimension.C. R. Acad. Sci. Paris Sér. I. Math., 316 (1993), 411–416. · Zbl 0805.20043 [28] Ghys, É. &de la Harpe, P. (editors),Sur les groupes hyperboliques d’après Mikhael Gromov. Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988. Progr. Math., 83. Birkhäuser, Boston, MA, 1990. [29] Gildenhuys, D. &Strebel, R., On the cohomology of soluble groups, II.J. Pure Appl. Algebra, 26 (1982), 293–323. · Zbl 0493.20032 [30] Gromov, M., Groups of polynomial growth and expanding maps.Inst. Hautes Études Sci. Publ. Math., 53 (1981), 53–73. · Zbl 0474.20018 [31] –, Asymptotic invariants of infinite groups, inGeometric Group Theory, Vol. 2 (Sussex, 1991), pp. 1–295. London Math. Soc. Lecture Note Ser., 182. Cambridge Univ. Press, Cambridge, 1993. [32] Guichardet, A.,Cohomologie des groupes topologiques et des algèbres de Lie. Textes Mathématiques, 2. CEDIC, Paris, 1980. · Zbl 0464.22001 [33] de la Harpe, P.,Topics in Geometric Group Theory. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. · Zbl 0965.20025 [34] de la Harpe, P. &Valette, A.,La propriété (T) de Kazhdan pour les groupes localement compacts. Astérisque, 175. Soc. Math. France, Paris, 1989. [35] Kapovich, M. & Kleiner, B., Coarse Alexander duality and duality groups. To appear inJ. Differential Geom. · Zbl 1086.57019 [36] Korevaar, N. J. &Schoen, R. M., Global existence theorems for harmonic maps to non-locally compact spaces.Comm. Anal. Geom., 5 (1997), 333–387. · Zbl 0908.58007 [37] Kropholler, P. H., Cohomological dimension of soluble groups.J. Pure Appl. Algebra, 43 (1986), 281–287. · Zbl 0603.20033 [38] Macdonald, I. D.,The Theory of Groups. Reprint of the 1968 original. Krieger, Malabar, FL, 1988. [39] Merzlyakov, Yu. I., Locally solvable groups of finite rank.Algebra i Logika Sem., 3 (1964), 5–16 (Russian). [40] Milnor, J., Growth of finitely generated solvable groups.J. Differential Geom., 2 (1968), 447–449. · Zbl 0176.29803 [41] Monod, N. & Shalom, Y., Orbit equivalence rigidity and bounded cohomology. To appear inAnn. of Math. · Zbl 1129.37003 [42] Montgomery, D. &Zippin, L.,Topological Transformation Groups. Reprint of the 1955 original. Krieger, Huntington, NY, 1974. · Zbl 0323.57023 [43] Mosher, L., Sageev, M. &Whyte, K., Quasi-actions on trees, I: Bounded valence.Ann. of Math., 158 (2003), 115–164. · Zbl 1038.20016 [44] Pansu, P., Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un.Ann. of Math., 129 (1989), 1–60. · Zbl 0678.53042 [45] Raghunathan, M. S.,Discrete Subgroups of Lie Groups. Ergeb. Math. Grenzgeb., 68. Springer-Verlag, New York-Heidelberg, 1972. · Zbl 0254.22005 [46] Reiter Ahlin, A., The large scale geometry of nilpotent-by-cyclic groups. Ph.D. Thesis, University of Chicago, 2002. · Zbl 1009.20033 [47] Rosenblatt, J. M., Invariant measures and growth conditions.Trans. Amer. Math. Soc., 193 (1974), 33–53. · Zbl 0246.28017 [48] Sela, Z., Uniform embeddings of hyperbolic groups in Hilbert spaces.Israel J. Math., 80 (1992), 171–181. · Zbl 0785.46032 [49] Shalom, Y., The growth of linear groups.J. Algebra, 199 (1998), 169–174. · Zbl 0892.20023 [50] –, Rigldity of commensurators and irreducible lattices.Invent. Math., 141 (2000), 1–54. · Zbl 0978.22010 [51] Stammbach, U., On the weak homological dimension of the group algebra of solvable groups.J. London Math. Soc., 2 (1970), 567–570. · Zbl 0204.35302 [52] Tits, J., Appendix to ”Groups of polynomial growth and expanding maps” by M. Gromov.Inst. Hautes Études Sci. Publ. Math., 53 (1981), 74–78. [53] Vershik, A. M. &Karpushev, S. I., Cohomology of groups in unitary representations, neighborhood of the identity and conditionally positive definite functions.Mat. Sb., 119 (161), (1982), 521–533. (Russian); English translation inMath. USSR-Sb., 47 (1984), 513–526. · Zbl 0513.43009 [54] Wolf, J. A., Growth of finitely generated solvable groups and curvature of Riemannian manifolds.J. Differential Geom., 2 (1968), 421–446. · Zbl 0207.51803 [55] Zimmer, R. J.,Ergodic Theory and Semisimple Groups. Monographs Math., 81. Birkhäuser, Basel, 1984. · Zbl 0571.58015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
# Automatically run program every 15 min

## Recommended Posts

Hello
I'm new to this and I tried to run my program every 15 min with @MIN and I did not succeed, could they help me?

##### Share on other sites

Welcome to our forum. Day ago I have the same concern as you have however, what I need is per day count, so, I use sleep() function to do my staff but @Melba23 responded me in my inquiry. So, basing of his idea, i made a simple timer that will run your program whenever you want to run your program within that day.

HotKeySet("{ESC}", "_Exit") ; just incase you want to end the program
$Mins = 15 ; this is where you add your @min$Timer = TimerInit()

While 1
If TimerDiff($Timer) > ($Mins * 60000) Then ; count per minute multiplied by 60sec.
ConsoleWrite("15 minutes have passed!" & @CRLF) ; console to see if running or what ever you wanted to do. Some staff
$Timer = TimerInit() EndIf WEnd Func _Exit() Exit EndFunc Here's my post if you like to have it per day count. KS15 #### Share this post ##### Link to post ##### Share on other sites 3 hours ago, Held51 said: I tried to run my program every 15 min with @MIN and I did not succeed, could they help me? Can you post your script so that we can have a look at what is going wrong? AutoIt.4.Life Clubrooms - Life is like a Donut (secret key) Spoiler Some messages & Apologizes: If I hurt you, Please accept my apologies, I never (regardless of the situation) mean to hurt anybody!!! Also, I am very busy with my project so I will appear in the last row of the online list, if you want to contact me: Email@TheDcoder.xyz Or you can have a nice chat with me in freenode, I use the same nick on freenode too! #### Share this post ##### Link to post ##### Share on other sites 8 hours ago, KickStarter15 said: Welcome to our forum. Day ago I have the same concern as you have however, what I need is per day count, so, I use sleep() function to do my staff but @Melba23 responded me in my inquiry. So, basing of his idea, i made a simple timer that will run your program whenever you want to run your program within that day. HotKeySet("{ESC}", "_Exit") ; just incase you want to end the program$Mins = 15 ; this is where you add your @min
$Timer = TimerInit() While 1 If TimerDiff($Timer) > ($Mins * 60000) Then ; count per minute multiplied by 60sec. ConsoleWrite("15 minutes have passed!" & @CRLF) ; console to see if running or what ever you wanted to do. Some staff$Timer = TimerInit()
EndIf
WEnd
Func _Exit()
Exit
EndFunc

Here's my post if you like to have it per day count.

KS15

Spoiler

I will always thank you for the time you spent for me.
I'm here to ask, and from your response, I'd like to learn.
By my knowledge, I can help someone else, and "that someone" could help in turn another, and so on.

##### Share on other sites

Yes, that would be great as well to use. But I still need to understand it first how it really works.

##### Share on other sites

Here's a template showing how I schedule my daily or weekly repeating tasks, at home and at work. Works like a charm. Just make sure that the Sleep value at the end of each task is at least 61 seconds [Sleep(61000)]; otherwise, you'll get more than one instance of the same task running simultaneously.

; Scheduler.au3
; Task Scheduler (AutoIt v3) [CLD rev.2/27/17]
; --------------------------------------------
#cs

Macro reference:
@YEAR       4-digit year
@MON        Month. Range: 01-12
@MDAY       Day of month. Range: 01-31
@HOUR       Hour. Range: 00-23
@MIN        Minutes. Range: 00-59
@SEC        Seconds. Range: 00-59
@MSEC       Millseconds. Range: 00-999
@WDAY       Numeric day of week. Range: 1-7 (Sunday-Saturday)
@YDAY       Day of year. Range: 001-366

#ce

#include <Misc.au3>
_Singleton(@ScriptName, 0)

; Machine ID variables
$bHome = False$bWork = False
Select
Case FileExists("d:\path\foo\*")
$bHome = True Case FileExists("e:\path\bar\*")$bWork = True
EndSelect

; Path variables
Select
Case $bHome$sXyDir = "d:\path\foo\xy"
$sLocateDir = "f:\Locate32"$svDosDir = "d:\path\foo\vDos"

Case $bWork$sXyDir = "d:\path\bar\xy"
$sLocateDir = "g:\Locate32"$svDosDir = "d:\path\bar\vDos"
EndSelect

; Other variables
$sNewsURL = "http://www.wnyc.org/stream/wnyc-fm939/windows.asx" ; ------------------------------------------------------------------- WHILE 1$iNow = @HOUR & @MIN

Select

Case $bHome And$iNow = 0000
SoundPlay($sXyDir & "\maid.mp3", 0) MsgBox(0, "It's Midnight...", "Time for sleep!", 60) Sleep(61000) Case$bHome And $iNow = 0005 ShellExecuteWait($sLocateDir & "\Updtdb32.exe")
Sleep(61000)

Case $bHome And @WDAY = 7 And$iNow = 0025
ShellExecute($svDosDir & "\VDP-checkinstall.exe") Sleep(61000) Case$bWork And ($iNow = 1108 Or$iNow = 1655)
Run($sLocateDir & "\Locate32.exe") Sleep(1000) WinActivate("Locate:") Sleep(2000) Send("{F9}") Sleep(5000) WinKill("Locate:") Sleep(100) WinActivate("vDos") Sleep(61000) Case$bWork And $iNow = 1800 Local$curw = WinGetTitle("[active]")
If WinActive("media player") Then
WinKill("media player")
Sleep(500)
EndIf
ShellExecute(@ScriptDir & "\start.exe", "_ " & $sNewsURL, @ScriptDir, "Open", 1) Sleep(3000) WinActivate("firefox") WinWaitActive("firefox") Sleep(500) Send("^w") WinActivate($curw)
Sleep(61000)

Case $bWork And$iNow = 1808
WinKill("media player")
Sleep(61000)

Case $bWork And$iNow = 1825
MsgBox(64, "Reminder: 6:25pm", "Time to go home!", 300)
Sleep(61000)

EndSelect

Sleep(500)
WEND

Edited by CarlD

##### Share on other sites
7 hours ago, KickStarter15 said:

Yes, that would be great as well to use. But I still need to understand it first how it really works.

Ahahahahahah

It's quite simple to use

Spoiler

I will always thank you for the time you spent for me.
I'm here to ask, and from your response, I'd like to learn.
By my knowledge, I can help someone else, and "that someone" could help in turn another, and so on.

##### Share on other sites

Yes, and getting started with it.

## Create an account

Register a new account

×

• Wiki

• Back

• Git

format: plain


text:
# Identity on sum over reciprocals of prime products?

The following identity seems to follow from a simple analysis of the sieve of Eratosthenes and inclusion-exclusion, where $p_i, p_j, p_k, \ldots$ denote primes and $N$ is an integer $\geq 2$:

$\Sigma_{p_i\leq N} \lfloor{N/p_i}\rfloor - \Sigma_{p_i, p_j\leq N} \lfloor{N/(p_i.p_j)}\rfloor + \Sigma_{p_i, p_j, p_k\leq N} \lfloor{N/(p_i.p_j.p_k)}\rfloor + \ldots = N - 1$

For example for $N = 6$, $\lfloor 6/2 \rfloor + \lfloor6/3\rfloor + \lfloor6/5\rfloor - \lfloor6/(3.2)\rfloor = 3 + 2 + 1 - 1 = 5 = 6 - 1$

Is this identity correct? If wrong, can it be fixed? If right, it must be well known -- so apologies in advance for a silly question, but is there a published reference? Also, is there any way to remove $N$ from the LHS so it becomes an identity/inequality only on sums of reciprocals of prime products?

• Legendre. Present in many books on primes and factorization. See e.g. Hans Riesel's book om computer methods, or Pomerance and Crandall's more recent text. – The Masked Avenger May 7 '14 at 17:07
• Also on wikipedia: en.wikipedia.org/wiki/Legendre_sieve – Terry Tao May 7 '14 at 20:51


text:
Browse

You are looking at 51 - 60 of 37,871 items for

• Refine by Access: all
Clear All
Free access

Neurosurgical management of patients with neurocutaneous melanosis: a systematic review

OBJECTIVE

Neurocutaneous melanocytosis (NCM), also referred to as neurocutaneous melanosis, is a rare neurocutaneous disorder characterized by excess melanocytic proliferation in the skin, leptomeninges, and cranial parenchyma. NCM most often presents in pediatric patients within the first 2 years of life and is associated with high mortality due to proliferation of melanocytes in the brain. Prognosis is poor, as patients typically die within 3 years of symptom onset. Due to the rarity of NCM, there are no specific guidelines for management. The aims of this systematic review were to investigate approaches toward diagnosis and examine modern neurosurgical management of NCM.

METHODS

A systematic review was performed using the PubMed database between April and December 2021 to identify relevant articles using PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines. Search criteria were created and checked independently among the authors. Inclusion criteria specified unique studies and case reports of NCM patients in which relevant neurosurgical management was considered and/or applied. Exclusion criteria included studies that did not report associated neurological diagnoses and neuroimaging findings, clinical reports without novel observations, and those unavailable in the English language. All articles that met the study inclusion criteria were included and analyzed.

RESULTS

A total of 26 extracted articles met inclusion criteria and were used for quantitative analysis, yielding a cumulative of 74 patients with NCM. These included 21 case reports, 1 case series, 2 retrospective cohort studies, 1 prospective cohort study, and 1 review. The mean patient age was 16.66 years (range 0.25–67 years), and most were male (76%). Seizures were the most frequently reported symptom (55%, 41/74 cases). Neurological diagnoses associated with NCM included epilepsy (45%, 33/74 cases), hydrocephalus (24%, 18/74 cases), Dandy-Walker malformation (24%, 18/74 cases), and primary CNS melanocytic tumors (23%, 17/74 cases). The most common surgical technique was CSF shunting (43%, 24/56 operations), with tethered cord release (4%, 2/56 operations) being the least frequently performed.

CONCLUSIONS

Current management of NCM includes CSF shunting to reduce intracranial pressure, surgery, chemotherapy, radiotherapy, immunotherapy, and palliative care. Neurosurgical intervention can aid in the diagnosis of NCM through tissue biopsy and resection of lesions with surgical decompression. Further evidence is required to establish the clinical outcomes of this rare entity and to describe the diverse spectrum of intracranial and intraspinal abnormalities present.

Free access

Free access

The role of frailty in the clinical management of neurofibromatosis type 1: a mixed-effects modeling study using the Nationwide Readmissions Database

OBJECTIVE

Frailty embodies a state of increased medical vulnerability that is most often secondary to age-associated decline. Recent literature has highlighted the role of frailty and its association with significantly higher rates of morbidity and mortality in patients with CNS neoplasms. There is a paucity of research regarding the effects of frailty as it relates to neurocutaneous disorders, namely, neurofibromatosis type 1 (NF1). In this study, the authors evaluated the role of frailty in patients with NF1 and compared its predictive usefulness against the Elixhauser Comorbidity Index (ECI).

METHODS

Publicly available 2016–2017 data from the Nationwide Readmissions Database was used to identify patients with a diagnosis of NF1 who underwent neurosurgical resection of an intracranial tumor. Patient frailty was queried using the Johns Hopkins Adjusted Clinical Groups frailty-defining indicator. ECI scores were collected in patients for quantitative measurement of comorbidities. Propensity score matching was performed for age, sex, ECI, insurance type, and median income by zip code, which yielded 60 frail and 60 nonfrail patients. Receiver operating characteristic (ROC) curves were created for complications, including mortality, nonroutine discharge, financial costs, length of stay (LOS), and readmissions while using comorbidity indices as predictor values. The area under the curve (AUC) of each ROC served as a proxy for model performance.

RESULTS

After propensity matching of the groups, frail patients had an increased mean ± SD hospital cost ($85,441.67 ±$59,201.09) compared with nonfrail patients ($49,321.77 ±$50,705.80) (p = 0.010). Similar trends were also found in LOS between frail (23.1 ± 14.2 days) and nonfrail (10.7 ± 10.5 days) patients (p = 0.0020). For each complication of interest, ROC curves revealed that frailty scores, ECI scores, and a combination of frailty+ECI were similarly accurate predictors of variables (p > 0.05). Frailty+ECI (AUC 0.929) outperformed using only ECI for the variable of increased LOS (AUC 0.833) (p = 0.013). When considering 1-year readmission, frailty (AUC 0.642) was outperformed by both models using ECI (AUC 0.725, p = 0.039) and frailty+ECI (AUC 0.734, p = 0.038).

CONCLUSIONS

These findings suggest that frailty and ECI are useful in predicting key complications, including mortality, nonroutine discharge, readmission, LOS, and higher costs in NF1 patients undergoing intracranial tumor resection. Consideration of a patient’s frailty status is pertinent to guide appropriate inpatient management as well as resource allocation and discharge planning.

Free access

The role of neurosurgery in the management of tuberous sclerosis complex–associated epilepsy: a systematic review

OBJECTIVE

Tuberous sclerosis complex (TSC) is an autosomal dominant, multisystem neurocutaneous disorder associated with cortical tubers, brain lesions seen in nearly all patients with TSC, which are frequently epileptogenic. Seizures are often the earliest clinical manifestation of TSC, leading to epilepsy in over 70% of patients. Medical management with antiepileptic drugs constitutes early therapy, but over 50% develop medically refractory epilepsy, necessitating surgical evaluation and treatment. The objective of this study was to summarize the literature and report seizure outcomes following surgical treatment for TSC-associated epilepsy.

METHODS

A systematic literature review was performed in accordance with the PRISMA guidelines. The PubMed and Embase databases were searched for journal articles reporting seizure outcomes following epilepsy surgery in TSC patients. Included studies were placed into one of two groups based on the surgical technique used. Excellent and worthwhile seizure reductions were defined for each group as outcomes and extracted from each study.

RESULTS

A total of 46 studies were included. Forty of these studies reported seizure outcomes following any combination of resection, disconnection, and ablation on a collective 1157 patients. Excellent and worthwhile seizure reductions were achieved in 59% (683/1157) and 85% (450/528) of patients, respectively. Six of these studies reported seizure outcomes following treatment with neuromodulation. Excellent and worthwhile seizure reductions were achieved in 34% (24/70) and 76% (53/70) of patients, respectively.

CONCLUSIONS

Surgery effectively controls seizures in select patients with TSC-associated epilepsy, but outcomes vary. Further understanding of TSC-associated epilepsy, improving localization strategies, and emerging surgical techniques represent promising avenues for improving surgical outcomes.

Restricted access

Apparent diffusion coefficient of piriform cortex and seizure outcome in mesial temporal lobe epilepsy after MR-guided laser interstitial thermal therapy: a single-institution experience

OBJECTIVE

Piriform cortex (PC) is one of the critical structures in the epileptogenesis of mesial temporal lobe epilepsy (mTLE), but its role is poorly understood. The authors examined the utility of apparent diffusion coefficient (ADC; an MR-based marker of tissue pathology) of the PC as a predictor of seizure outcome in patients with mTLE undergoing MR-guided laser interstitial thermal therapy (MRgLITT).

METHODS

A total of 33 patients diagnosed with mTLE who underwent MRgLITT at the authors’ institution were included in the study. The 6-month postoperative seizure outcomes were classified using the International League Against Epilepsy (ILAE) system as good (complete seizure freedom, ILAE class I) and poor (seizure present, ILAE classes II–VI). The PC and ablation volumes were manually segmented from both the preoperative and intraoperative MRI sequences, respectively. The mean ADC intensities of 1) preablation PC; 2) total ablation volume; 3) ablated portion of PC; and 4) postablation residual PC were calculated and compared between good and poor outcome groups. Additionally, the preoperative PC volumes and proportion of PC volume ablated were examined and compared between the subjects in the two outcome groups.

RESULTS

The mean age at surgery was 36.5 ± 3.0 years, and the mean follow-up duration was 1.9 ± 0.2 years. Thirteen patients (39.4%) had a good outcome. The proportion of PC ablated was significantly associated with seizure outcome (10.16 vs 3.30, p < 0.05). After accounting for the variability in diffusion tensor imaging acquisition parameters, patients with good outcome had a significantly higher mean ADC of the preablation PC (0.3770 vs −0.0108, p < 0.05) and the postoperative residual PC (0.4197 vs 0.0309, p < 0.05) regions compared to those with poor outcomes. No significant differences in ADC of the ablated portion of PC were observed (0.2758 vs −0.4628, p = 0.12) after performing multivariate analysis.

CONCLUSIONS

A higher proportion of PC ablated was associated with complete seizure freedom. Preoperative and postoperative residual ADC measures of PC were significantly higher in the good seizure outcome group in patients with mTLE who underwent MRgLITT, suggesting that ADC analysis can assist with postablation outcome prediction and patient stratification.

Restricted access

Complex cranial surgery and the future of open cerebrovascular training

Restricted access

Decompressive hemicraniectomy and cranioplasty using subcutaneously preserved autologous bone flaps versus synthetic implants: perioperative outcomes and cost analysis

OBJECTIVE

It has not been well-elucidated whether there are advantages to preserving bone flaps in abdominal subcutaneous (SQ) tissue after decompressive hemicraniectomy (DHC), compared to discarding bone flaps. The authors aimed to compare perioperative outcomes and costs for patients undergoing autologous cranioplasty (AC) after DHC with the bone flap preserved in abdominal SQ tissue, and for patients undergoing synthetic cranioplasty (SC).

METHODS

A retrospective review was performed of all patients undergoing DHC procedures between January 2017 and July 2021 at two tertiary care institutions. Patients were divided into two groups: those with flaps preserved in SQ tissue (SQ group), and those with the flap discarded (discarded group). Additional analysis was performed between patients undergoing AC versus SC. Primary end points included postoperative and surgical site complications. Secondary endpoints included operative costs, length of stay, and blood loss.

RESULTS

A total of 248 patients who underwent DHC were included in the study, with 155 patients (62.5%) in the SQ group and 93 (37.5%) in the discarded group. Patients in the discarded group were more likely to have a diagnosis of severe TBI (57.0%), while the most prevalent diagnosis in the SQ group was malignant stroke (35.5%, p < 0.05). There were 8 (5.2%) abdominal surgical site infections and 9 (5.8%) abdominal hematomas. The AC group had a significantly higher reoperation rate (23.2% vs 12.9%, p = 0.046), with 11% attributable to abdominal reoperations. The average cost of a reoperation for an abdominal complication was $40,408.75 ±$2273. When comparing the AC group to the SC group after cranioplasty, there were no significant differences in complications or surgical site infections. There were 6 cases of significant bone resorption requiring cement supplementation or discarding of the bone flap. Increased mean operative charges were found for the SC group compared to the AC group ($72,362 vs$59,726, p < 0.001).

CONCLUSIONS

Autologous bone flaps may offer a cost-effective option compared to synthetic flaps. However, when preserved in abdominal SQ tissue, they pose the risk of resorption over time as well as abdominal surgical site complications with increased reoperation rates. Further studies and methodologies such as cryopreservation of the bone flap may be beneficial to reduce costs and eliminate complications associated with abdominal SQ storage.

Restricted access

Endoscope-assisted visualization of 5-aminolevulinic acid fluorescence in surgery for brain metastases

OBJECTIVE

Fluorescence-guided resection of cerebral metastases has been proposed as an approach to visualize residual tumor tissue and maximize the extent of resection. Critics have argued that tumor cells at the resection margins might be overlooked under microscopic visualization because of technical limitations. Therefore, an endoscope, which is capable of inducing fluorescence, has been applied with the aim of improving exposure of fluorescent tumor tissue. In this retrospective analysis, authors assessed the utility of endoscope assistance in 5-aminolevulinic acid (5-ALA) fluorescence–guided resection of brain metastases.

METHODS

Between June 2013 and December 2016, a standard 20-mg/kg dose of 5-ALA was administered 4 hours prior to surgery in 26 patients with suspected single brain metastases. After standard neuronavigated microsurgical tumor resection, a microscope capable of inducing fluorescence was used to examine tumor margins. The authors classified the remaining fluorescence into 3 grades (0 = none, 1 = weak, and 2 = strong). Endoscopic assistance was employed if no or only weak fluorescence was visualized at the resection margins under the microscope. Endoscopically identified fluorescent tissue at the margins was resected and evaluated separately via histological examination to prove or disprove tumor infiltration.

RESULTS

Under the microscope, weakly fluorescent tissue was seen at the margins of the resection cavity in 15/26 (57.7%) patients. In contrast, endoscopic inspection revealed strongly fluorescent tissue in 22/26 (84.6%) metastases. In 11/26 (42.3%) metastases no fluorescence at the tumor margins was detected by the microscope; however, strong fluorescence was visualized under the endoscope in 7 (63.6%) of these 11 metastases. In the 15 metastases with microscopically weak fluorescence, strong fluorescence was seen when using the endoscope. Neither microscopic nor endoscopic fluorescence was found in 4/26 (15.4%) cases. In the 26 patients, 96 histological specimens were obtained from the margins of the resection cavity. Findings from these specimens were in conjunction with the histopathological findings, allowing identification of metastatic infiltration with a sensitivity of 95.5% and a specificity of 75% using endoscope assistance.

CONCLUSIONS

Fluorescence-guided endoscope assistance may overcome the technical limitations of the conventional microscopic exposure of 5-ALA–fluorescent metastases and thereby increase visualization of fluorescent tumor tissue at the margins of the resection cavity with high sensitivity and acceptable specificity.

Restricted access

Factors associated with preoperative and postoperative seizures in patients undergoing resection of brain metastases

OBJECTIVE

Epileptic seizures are a common and potentially devastating complication of metastatic brain tumors. Although tumor-related seizures have been described in previous case series, most studies have focused on primary brain tumors and have not differentiated between different types of cerebral metastases. The authors analyzed a large surgical cohort of patients with brain metastases to examine risk factors associated with preoperative and postoperative seizures and to better understand the seizure risk factors of metastatic brain tumors.

METHODS

Patients who underwent resection of a brain metastasis at the University of California, San Francisco (UCSF), were retrospectively reviewed. Patients included in the study were ≥ 18 years of age, required resection of a brain metastasis, and were treated at UCSF. Primary cancers included melanoma, non–small cell lung adenocarcinoma, breast adenocarcinoma, colorectal adenocarcinoma, esophageal adenocarcinoma, gastric adenocarcinoma, renal cell carcinoma, urothelial carcinoma, ovarian carcinoma, cervical squamous cell carcinoma, and endometrial adenocarcinoma. Patients were evaluated for primary cancer type and seizure occurrence, as well as need for use of antiepileptic drugs preoperatively, at time of discharge, and at 6 months postoperatively. Additionally, Engel classification scores were assigned to those patients who initially presented with seizures preoperatively. Univariate and multivariate regression analyses were used to assess the association of tumor type with preoperative seizures.

RESULTS

Data were retrospectively analyzed for 348 consecutive patients who underwent surgical treatment of brain metastases between 1998 and 2019. The cohort had a mean age of 60 years at the time of surgery and was 59% female. The mean and median follow-up durations after the date of surgery for the cohort were 22 months and 10.8 months, respectively. In univariate analysis, frontal lobe location (p = 0.05), melanoma (p = 0.02), KRAS mutation in lung carcinoma (p = 0.04), intratumoral hemorrhage (p = 0.04), and prior radiotherapy (p = 0.04) were associated with seizure presentation. Postoperative checkpoint inhibitor use (p = 0.002), prior radiotherapy (p = 0.05), older age (p = 0.002), distant CNS progression (p = 0.004), and parietal lobe tumor location (p = 0.002) were associated with seizures at 6 months postoperatively. The final multivariate model confirmed the independent effects of tumor location in the frontal lobe and presence of intratumoral hemorrhage as predictors of preoperative seizures, and checkpoint inhibitor use and parietal lobe location were identified as significant predictors of seizures at 6 months postoperatively.

CONCLUSIONS

Within this surgical cohort of patients with brain metastases, seizures were seen in almost a quarter of patients preoperatively. Frontal lobe metastases and hemorrhagic tumors were associated with higher risk of preoperative seizures, whereas checkpoint inhibitor use and parietal lobe tumors appeared to be associated with seizures at 6 months postoperatively. Future research should focus on the effect of metastatic lesion–targeting therapeutic interventions on seizure control in these patients.

Restricted access

Giant cerebral cavernous malformations: redefinition based on surgical outcomes and systematic review of the literature

OBJECTIVE

Giant cerebral cavernous malformations (GCCMs) are rare vascular malformations. Unlike for tumors and aneurysms, there is no clear definition of a "giant" cavernous malformation (CM). As a result of variable definitions, working descriptions and outcome data of patients with GCCM are unclear. A new definition of GCCM related to surgical outcomes is needed.

METHODS

An institutional database was searched for all patients who underwent resection of CMs > 1 cm in diameter. Patient information, surgical technique, and clinical and radiographic outcomes were assessed. A systematic review was performed to augment an earlier published review.

RESULTS

In the authors’ institutional cohort of 183 patients with a large CM, 179 with preoperative and postoperative modified Rankin Scale (mRS) scores were analyzed. A maximum CM diameter of ≥ 3 cm was associated with greater risk of severe postoperative decline (≥ 2-point increase in mRS score). After adjustment for age and deep versus superficial location, size ≥ 3 cm was strongly predictive of severe postoperative decline (OR 4.5, 95% CI 1.2–16.9). A model with CM size and deep versus superficial location was developed to predict severe postoperative decline (area under the receiver operating characteristic curve 0.79). Thirteen more patients with GCCMs have been reported in the literature since the most recent systematic review, including some patients who were treated earlier and not discussed in the previous review.

CONCLUSIONS

The authors propose that cerebral CMs with a diameter ≥ 3 cm be defined as GCCMs on the basis of the inflection point for functional and neurological outcomes. This definition is in line with the definitions for other giant lesions. It is less exclusive than earlier definitions but captures the rarity of these lesions (approximately 1% incidence) and variation in outcomes. GCCMs remain operable with potentially favorable outcomes. The term "giant" is not meant to deter or contraindicate surgery.


text:
## Thursday, January 27, 2011

### Generate Test Files From the Command Line

Note to self: I had to generate some files quickly to test the behavior of the .NET FileSystemWatcher. This little bash script will create 6 zero-filled files of of size $$2 \times 10^i$$ KiB, where $$i \in \{0, 1, \dots, 5\}$$.


text:
Macro to do nothing via a \def

I have encountered another expansion issue and have narrowed it down to this simple test case of a macro that does nothing, well at least it tries to do nothing, but is not all that successful.

If I declare this macro as:

\newcommand*{\DoNothingA}[1]{#1}%

This works great, no surprises there.

However, if this macros is defined as follows:

\newcommand*{\DoNothingB}[1]{%
\def\Temp{#1}%
\Temp%
}%

then, this has problems where there is an attempt to use this in an \edef.

Output:

Note that the MWE below yields a compile error for the last step, so you need to hit <RETURN> to skip past it to see the output (or comment out the last \edef, but then this won't show Question 2 below).

The MWE below yields the following:

The last line being especially curious as it produced foo 4, and was the result of:

\edef\NewTemp{\DoNothingA{foo 5}}
\NewTemp
\color{red}% Highlight problem output
\edef\NewTemp{\DoNothingB{foo 6}}
\NewTemp
\color{black}
~-- used \verb|\edef| to store output of macro

Questions:

1. What is the explanation of the expansion issue here?
2. How does the final output become foo 4 (foo 5 would have been easier to accept), if we skip past the compile error?
3. Since David Carlisle has been quoted as saying that "a few extra \expandafter cure all known ills" :-), what is the sequence of \expandafters needed in the last \edef to use macro \DoNothinB as defined here.
4. How can I adjust the \DoNothingB{} macro to use a temp variable and still work in the three cases in the MWE (preferrably without having to use any \expandafter trickery.

Code:

\documentclass{article}
\usepackage{xcolor}% To highlight problem output

\newcommand*{\DoNothingA}[1]{#1}% Does everything I want in all cases

\newcommand*{\DoNothingB}[1]{% Works mostly, except if used in a \edef
\def\Temp{#1}%
\Temp%
}%

\begin{document}
% These two work great.
\DoNothingA{foo 1}
\DoNothingB{foo 2}
-- used output of macro directly

% These two also work great.
\def\NewTemp{\DoNothingA{foo 3}}
\NewTemp
\def\NewTemp{\DoNothingB{foo 4}}
\NewTemp
~-- used \verb|\def| to store output of macro

\edef\NewTemp{\DoNothingA{foo 5}}
\NewTemp
\color{red}% Highlight problem output
\edef\NewTemp{\DoNothingB{foo 6}}
%\show\NewTemp% Excellent suggestion by David Carlisle yields: \def foo 4{foo 6}foo 4
\NewTemp
\color{black}
~-- used \verb|\edef| to store output of macro
% Why is the last output "foo 4" (after ignoring error)??
\end{document}

-

2 Answers

Short answer: You can't use assignments like \def or \edef inside expandable contexts like \edef because they are not expandable!

Long answer:
An \edef expands its content until only non-expandable tokens are left (note that text is not expandable). \def is an assignment and all assignments must be executed and are therefore not expandable. Your \DoNothingB actually does something: it defines \Temp!

Let me explain what happens on the following example:

\def\Temp{before}
% ...
\edef\NewTemp{\def\Temp{something}}

then the \edef tries to expand first \def which is not expandable and therefore stays at it is, then \temp which is expanded to before and then the rest: the tokens {, s, o, ..., g, and }, which are all not expandable either. Therefore you get \NewTemp as \def before{something} which will instruct TeX, once \NewTemp is expanded, i.e. used, to define b with the parameter text efore and the replacement text something. Because b is immutable (as long it is not declared an active character) you will get an error here.

In your example \Temp has been define to foo 4 in your fourth example, where you use \DoNothingB outside of an \edef. In the next usage inside of an \edef (\edef\NewTemp{\DoNothingB{foo 6}}) you get \def foo4{foo 6}foo4 for \NewTemp because both \Temp usage are expanded right then, which leads to the above mentioned error. The \def foo4{foo 6} is discarded as part of the error handling and then foo4 is typeset. If \Temp would be defined differently before the output would be accordantly.

A few \expandafters don't help you here because the order is not the issue here and \edef expands anyway everything continuously until only non-expandable tokens remain.

However, you might want to add some \noexpand direct before the \Temp macros inside \DoNothingB to protect them from premature expansion in the first \edef. This now doesn't work inside a \def. Normally you can use \protect with LaTeX's \protected@edef instead. Depending on the context \protect is either \relax (outside \protected@edef) or \@unexpandable@protect (inside \protected@edef) which is similar to \noexpand. For usage with \def you need to test this mode by yourself and add a \noexpand manually if inside edef.

The following code does this. Note that you need to replace all \edefs with \protected@edef for this to work. The normal \edef and other expanding contexts like \message or \write will not work.

\documentclass{article}
\usepackage{xcolor}% To highlight problem output

\newcommand*{\DoNothingA}[1]{#1}% Does everything I want in all cases

\makeatletter
\newcommand*{\DoNothingB}[1]{% Works mostly, except if used in a \edef
\ifx\protect\@unexpandable@protect
\def\noexpand\Temp{#1}%
\else
\def\Temp{#1}%
\fi
\protect\Temp%
}%
\makeatother

\begin{document}
% These two work great.
\DoNothingA{foo 1}
\DoNothingB{foo 2}
-- used output of macro directly

% These two also work great.
\def\NewTemp{\DoNothingA{foo 3}}
\NewTemp
\def\NewTemp{\DoNothingB{foo 4}}
\NewTemp
~-- used \verb|\def| to store output of macro

\edef\NewTemp{\DoNothingA{foo 5}}
\NewTemp
\color{red}% Highlight problem output
\makeatletter
\protected@edef\NewTemp{\DoNothingB{foo 6}}
\makeatother
\NewTemp
\color{black}
~-- used \verb|\edef| to store output of macro
% Why is the last output "foo 4" (after ignoring error)??
\end{document}

-
\newcommand*{\DoNothingA}[1]{#1}

\newcommand*{\DoNothingB}[1]{\def\Temp{#1}\Temp}

\begin{document}

\DoNothingA{foo 1}
\DoNothingB{foo 2}

According to the definitions this prints "foo 1" and "foo 2" and defines \Temp to expand to foo 2

\def\NewTemp{\DoNothingA{foo 3}}
\NewTemp

This defines \NewTemp to expand to \DoNothingA{foo 3}, so \NewTemp prints "foo 3"

\def\NewTemp{\DoNothingB{foo 4}}
\NewTemp

This does

\DoNothingB{foo 4}

which defines \Temp to expand to foo 4 and prints "foo 4"

\edef\NewTemp{\DoNothingA{foo 5}}
\NewTemp

Let's go slowly here. The \edef causes the expansion of \DoNothingA, which finds it argument and is replaced by its replacement text; all is eventually equivalent to saying

\def\NewTemp{foo 5}

Now the fun begins.

\edef\NewTemp{\DoNothingB{foo 6}}

Here \DoNothingB finds its argument and is replaced by

\def\Temp{foo 6}\Temp

but \edef is not satisfied and replaces both instances of \Temp by its replacement text, which is still foo 4 and so TeX executes the equivalent of

\def\NewTemp{\def foo4{foo 6}foo 4}

and now the call

\NewTemp

will try doing

\def foo4{foo 6}foo 4

The result is an error message: since no control sequence follows \def, TeX inserts \inaccessible and performs

\def\inaccessible foo4{foo 6}foo 4

which results in printing "foo 4" after having defined the \inaccessible control sequence.

So there are the answers to 1 and 2. The answers to 3 and 4 are easy: you can't perform an assignment during an \edef, with any number of \expandafters, because TeX doesn't perform assignments during expansion, but only at a later stage of processing. In summary: you can't change the meaning of a control sequence while doing an \edef.

Workaround

If you want to feed \DoNothingB in an \edef you have to decide what it's supposed to do in that case. If you simply want that it does nothing special with respect to being inside a \def then

\protected\def\Temp{} % initialization
\newcommand*\DoNothingB[1]{\protected\def\Temp{#1}\Temp}

might do; if you say

\edef\NewTemp{\DoNothingB{foo}}

this would expand \DoNothingB resulting in the token list

\protected\def\Temp{foo}\Temp

but now all tokens are unexpandable and so the \edef would be equivalent to

\def\NewTemp{\protected\def\Temp{foo}\Temp}

In case of \def\NewTemp{\DoNothingB{foo}} a call of \NewTemp would do the same as before after the first expansion step. Note that it's necessary to initialize \Temp to be a \protected macro, otherwise something like

\edef\NewTemp{\DoNothingB{foo}}

would result in an error message about "Undefined control sequence".

Of course, this is under the assumption that the argument to \DoNothingB is made of unexpandable tokens, as they wouldn't be protected against expansion.

-


text:
# Which among the following is the fundamental quantity ?

Which among the following is the fundamental quantity?

(1) Volume

(2) Time

(3) Velocity

(4) Force

Answer: (2). The fundamental qualities of Physics are the seven basic quantities that can be used to express all other physical quantities. These are as follows: Length: Metre, Heat: Kelvin, Time: second, Luminous Intensity: Candela, Mass: Kilogram, Electric Current: Ampere, and Amount of substance: Moles.


text:
# Part 6.2Using MySQL queries in PHP

Queries that have been generated would be useless if they could not be output or worked on with PHP.

## Sample queries

Below are some sample queries that will be referenced in this article ($query1 and $query2):

PHP
<?php
$myConnection = mysqli_connect($dbName, $dbUsername,$dbPassword);

$query1 = "SELECT * FROM table1 WHERE id > 4";$query2 = "SELECT * FROM table1 WHERE forename = 'John'";

$result1 = mysqli_query($myConnection, $query1); if(!$result1)
echo "Failure!";

$result2 = mysqli_query($myConnection, $query2); if(!$result2)
echo "Failure!";

mysqli_close($myConnection); ?>  Assume that the following table ("table1") has been used: id forename surname age 0 James Adams 44 1 Frank Adams 45 2 John Roosevelt 45 3 Mark French 46 4 Frank Skeldon 43 5 Justin McGregor 51 6 Helga Adams 45 7 John Smith 46 ## Working with the result The important note is that the information that has been retrieved from the server is now in the $result1 and $result2 variables. This means that any kind of references to the database data will only refer to the variables. If the database changes after the query, these changes will not be reflected in the variables. ## Count the number of results MySQL can count the number of rows using the COUNT aggregate function. This may be useful if all that is required is the count of the results but in cases where the information is required multiple times this would be slower than using PHP to count them. PHP provides the mysqli_num_rows function to get the number of rows found in a query: PHP <?php //Should output 3 echo mysqli_num_rows($result1);
//Should output 2
}
?>

## Getting the results from the query

Of course, none of these functions have worked on the actual result, giving out the values returned. This is achieved, mostly, using the mysqli_fetch_array function.

This function transforms the result into a PHP array. Each row itself is an associative array. This means that the result can be iterated with a foreach loop:

PHP
<?php
$rows = mysqli_fetch_array($result1);

foreach($rows as$row) {
//Will output the id column
echo $row[0]; //Will output the forename column echo$row[1];
}
?>

Alternatively, the column name can be used instead of using the index of the column:

PHP
<?php
$rows = mysqli_fetch_array($result1);

foreach($rows as$row) {
//Will output the id column
echo $row['id']; //Will output the forename column echo$row['forename'];
}
?>

Code preview
Feedback 👍
Comments are sent via email to me.


text:
# methods

0th

Percentile

##### Methods for Gradient Boosting Objects

Methods for models fitted by boosting algorithms.

Keywords
methods
##### Usage
# S3 method for glmboost
print(x, ...)
# S3 method for mboost
print(x, ...)# S3 method for mboost
summary(object, ...)# S3 method for mboost
coef(object, which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)
# S3 method for glmboost
coef(object, which = NULL,
aggregate = c("sum", "cumsum", "none"), off2int = FALSE, ...)# S3 method for mboost
[(x, i, return = TRUE, ...)
mstop(x) <- value# S3 method for mboost
AIC(object, method = c("corrected", "classical", "gMDL"),
df = c("trace", "actset"), ..., k = 2)# S3 method for mboost
mstop(object, ...)
# S3 method for gbAIC
mstop(object, ...)
# S3 method for cvrisk
mstop(object, ...)# S3 method for mboost
predict(object, newdata = NULL,
type = c("link", "response", "class"), which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)
# S3 method for glmboost
predict(object, newdata = NULL,
type = c("link", "response", "class"), which = NULL,
aggregate = c("sum", "cumsum", "none"), ...)# S3 method for mboost
fitted(object, ...)# S3 method for mboost
residuals(object, ...)
# S3 method for mboost
resid(object, ...)# S3 method for glmboost
variable.names(object, which = NULL, usedonly = FALSE, ...)
# S3 method for mboost
variable.names(object, which = NULL, usedonly = FALSE, ...)# S3 method for mboost
extract(object, what = c("design", "penalty", "lambda", "df",
"coefficients", "residuals",
"variable.names", "bnames", "offset",
"nuisance", "weights", "index", "control"),
which = NULL, ...)
# S3 method for glmboost
extract(object, what = c("design", "coefficients", "residuals",
"variable.names", "offset",
"nuisance", "weights", "control"),
which = NULL, asmatrix = FALSE, ...)
# S3 method for blg
extract(object, what = c("design", "penalty", "index"),
asmatrix = FALSE, expand = FALSE, ...)# S3 method for mboost
logLik(object, ...)
# S3 method for gamboost
hatvalues(model, ...)
# S3 method for glmboost
hatvalues(model, ...)# S3 method for mboost
selected(object, ...)# S3 method for mboost
risk(object, ...)# S3 method for mboost
nuisance(object)downstream.test(object, ...)
##### Arguments
object

objects of class glmboost, gamboost, blackboost or gbAIC.

x

objects of class glmboost or gamboost.

model

objects of class mboost

newdata

optionally, a data frame in which to look for variables with which to predict. In case the model was fitted using the matrix interface to glmboost, newdata must be a matrix as well (an error is given otherwise).

which

a subset of base-learners to take into account for computing predictions or coefficients. If which is given (as an integer vector or characters corresponding to base-learners) a list or matrix is returned.

usedonly

logical. Indicating whether all variable names should be returned or only those selected in the boosting algorithm.

type

the type of prediction required. The default is on the scale of the predictors; the alternative "response" is on the scale of the response variable. Thus for a binomial model the default predictions are of log-odds (probabilities on logit scale) and type = "response" gives the predicted probabilities. The "class" option returns predicted classes.

aggregate

a character specifying how to aggregate predictions or coefficients of single base-learners. The default returns the prediction or coefficient for the final number of boosting iterations. "cumsum" returns a list with matrices (one per base-learner) with the cumulative coefficients for all iterations simultaneously (in columns). "none" returns a list of matrices where the $j$th columns of the respective matrix contains the predictions of the base-learner of the $j$th boosting iteration (and zero if the base-learner is not selected in this iteration).

off2int

logical. Indicating whether the offset should be added to the intercept (if there is any) or if the offset is returned as attribute of the coefficient (default).

i

integer. Index specifying the model to extract. If i = 0, the offset model is returned. If i is smaller than the initial mstop, a subset is used. If i is larger than the initial mstop, additional boosting steps are performed until step i is reached. See details for more information.

value

integer. See i.

return

a logical indicating whether the changed object is returned.

method

a character specifying if the corrected AIC criterion or a classical (-2 logLik + k * df) should be computed.

df

a character specifying how degrees of freedom should be computed: trace defines degrees of freedom by the trace of the boosting hat matrix and actset uses the number of non-zero coefficients for each boosting iteration.

k

numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC. Only used when method = "classical".

what

a character specifying the quantities to extract. Depending on object this can be a subset of "design" (default; design matrix), "penalty" (penalty matrix), "lambda" (smoothing parameter), "df" (degrees of freedom), "coefficients", "residuals", "variable.names", "bnames" (names of the base-learners), "offset", "nuisance", "weights", "index" (index of ties used to expand the design matrix) and "control". In future versions additional extractors might be specified.

asmatrix

a logical indicating whether the the returned matrix should be coerced to a matrix (default) or if the returned object stays as it is (i.e., potentially a sparse matrix). This option is only applicable if extract returns matrices, i.e., what = "design" or what = "penalty".

expand

a logical indicating whether the design matrix should be expanded (default: FALSE). This is useful if ties where taken into account either manually (via argument index in a base-learner) or automatically for data sets with many observations. expand = TRUE is equivalent to extract(B)[extract(B, what = "index"),] for a base-learner B.

##### Details

These functions can be used to extract details from fitted models. print shows a dense representation of the model fit and summary gives a more detailed representation.

The function coef extracts the regression coefficients of a linear model fitted using the glmboost function or an additive model fitted using the gamboost. Per default, only coefficients of selected base-learners are returned. However, any desired coefficient can be extracted using the which argument (see examples for details). Per default, the coefficient of the final iteration is returned (aggregate = "sum") but it is also possible to return the coefficients from all iterations simultaniously (aggregate = "cumsum"). If aggregate = "none" is specified, the coefficients of the selected base-learners are returned (see examples below). For models fitted via glmboost with option center = TRUE the intercept is rarely selected. However, it is implicitly estimated through the centering of the design matrix. In this case the intercept is always returned except which is specified such that the intercept is not selected. See examples below.

The predict function can be used to predict the status of the response variable for new observations whereas fitted extracts the regression fit for the observations in the learning sample. For predict newdata can be specified, otherwise the fitted values are returned. If which is specified, marginal effects of the corresponding base-learner(s) are returned. The argument type can be used to make predictions on the scale of the link (i.e., the linear predictor $X\beta$), the response (i.e. $h(X\beta)$, where h is the response function) or the class (in case of classification). Furthermore, the predictions can be aggregated analogously to coef by setting aggregate to either sum (default; predictions of the final iteration are given), cumsum (predictions of all iterations are returned simultaniously) or none (change of prediction in each iteration). If applicable the offset is added to the predictions. If marginal predictions are requested the offset is attached to the object via attr(..., "offset") as adding the offset to one of the marginal predictions doesn't make much sense.

The [.mboost function can be used to enhance or restrict a given boosting model to the specified boosting iteration i. Note that in both cases the original x will be changed to reduce the memory footprint. If the boosting model is enhanced by specifying an index that is larger than the initial mstop, only the missing i - mstop steps are fitted. If the model is restricted, the spare steps are not dropped, i.e., if we increase i again, these boosting steps are immediately available. Alternatively, the same operation can be done by mstop(x) <- i.

The residuals function can be used to extract the residuals (i.e., the negative gradient of the current iteration). resid is is an alias for residuals.

Variable names (including those of interaction effects specified via by in a base-learner) can be extracted using the generic function variable.names, which has special methods for boosting objects.

The generic extract function can be used to extract various characteristics of a fitted model or a base-learner. Note that the sometimes a penalty function is returned (e.g. by extract(bols(x), what = "penalty")) even if the estimation is unpenalized. However, in this case the penalty paramter lambda is set to zero. If a matrix is returned by extract one can to set asmatrix = TRUE if the returned matrix should be coerced to class matrix. If asmatrix = FALSE one might get a sparse matrix as implemented in package Matrix. If one requests the design matrix (what = "design") expand = TRUE expands the resulting matrix by taking the duplicates handeled via index into account.

The ids of base-learners selected during the fitting process can be extracted using selected(). The nuisance() method extracts nuisance parameters from the fit that are handled internally by the corresponding family object, see "'>boost_family". The risk() function can be used to extract the computed risk (either the "inbag" risk or the "oobag" risk, depending on the control argument; see boost_control).

For (generalized) linear and additive models, the AIC function can be used to compute both the classical AIC (only available for familiy = Binomial() and familiy = Poisson()) and corrected AIC (Hurvich et al., 1998, only available when family = Gaussian() was used). Details on the used approximations for the hat matrix can be found in Buehlmann and Hothorn (2007). The AIC is useful for the determination of the optimal number of boosting iterations to be applied (which can be extracted via mstop). The degrees of freedom are either computed via the trace of the boosting hat matrix (which is rather slow even for moderate sample sizes) or the number of variables (non-zero coefficients) that entered the model so far (faster but only meaningful for linear models fitted via gamboost (see Hastie, 2007)). For a discussion of the use of AIC based stopping see also Mayr, Hofner and Schmid (2012).

In addition, the general Minimum Description Length criterion (Buehlmann and Yu, 2006) can be computed using function AIC.

Note that logLik and AIC only make sense when the corresponding Family implements the appropriate loss function.

downstream.test computes tests for linear models fitted via glmboost with a likelihood based loss function and only suitable without early stopping, i.e., if likelihood based model converged. In order to work, the Fisher matrix must be implemented in the Family; currently this is only the case for family RCG.

##### Note

The [.mboost function changes the original object, i.e. gbmodel[10] changes gbmodel directly!

##### Warning

The coefficients resulting from boosting with family Binomial(link = "logit") are $1/2$ of the coefficients of a logit model obtained via glm (see Binomial).

##### References

Benjamin Hofner, Andreas Mayr, Nikolay Robinzonov and Matthias Schmid (2014). Model-based Boosting in R: A Hands-on Tutorial Using the R Package mboost. Computational Statistics, 29, 3--35. http://dx.doi.org/10.1007/s00180-012-0382-5

Clifford M. Hurvich, Jeffrey S. Simonoff and Chih-Ling Tsai (1998), Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society, Series B, 20(2), 271--293.

Peter Buehlmann and Torsten Hothorn (2007), Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22(4), 477--505.

Trevor Hastie (2007), Discussion of Boosting algorithms: Regularization, prediction and model fitting'' by Peter Buehlmann and Torsten Hothorn. Statistical Science, 22(4), 505.

Peter Buehlmann and Bin Yu (2006), Sparse boosting. Journal of Machine Learning Research, 7, 1001--1024.

Andreas Mayr, Benjamin Hofner, and Matthias Schmid (2012). The importance of knowing when to stop - a sequential stopping rule for component-wise gradient boosting. Methods of Information in Medicine, 51, 178--186. DOI: http://dx.doi.org/10.3414/ME11-02-0030

gamboost, glmboost and blackboost for model fitting.

plot.mboost for plotting methods.

cvrisk for cross-validated stopping iteration.

##### Aliases
• mboost_methods
• print.glmboost
• print.mboost
• summary.mboost
• coef.mboost
• coef.glmboost
• [.mboost
• AIC.mboost
• mstop
• mstop.gbAIC
• mstop.mboost
• mstop.cvrisk
• mstop<-
• predict.mboost
• predict.gamboost
• predict.blackboost
• predict.glmboost
• fitted.mboost
• residuals.mboost
• resid.mboost
• variable.names.glmboost
• variable.names.mboost
• risk
• risk.mboost
• extract
• extract.mboost
• extract.gamboost
• extract.glmboost
• extract.blackboost
• extract.blg
• extract.bl_lin
• extract.bl_tree
• logLik.mboost
• hatvalues.gamboost
• hatvalues.glmboost
• selected
• selected.mboost
• nuisance
• nuisance.mboost
• downstream.test
##### Examples
# NOT RUN {
### a simple two-dimensional example: cars data
cars.gb <- glmboost(dist ~ speed, data = cars,
control = boost_control(mstop = 2000),
center = FALSE)
cars.gb

### initial number of boosting iterations
mstop(cars.gb)

### AIC criterion
aic <- AIC(cars.gb, method = "corrected")
aic

### extract coefficients for glmboost
coef(cars.gb)
coef(cars.gb, off2int = TRUE)        # offset added to intercept
coef(lm(dist ~ speed, data = cars))  # directly comparable

cars.gb_centered <- glmboost(dist ~ speed, data = cars,
center = TRUE)
selected(cars.gb_centered)           # intercept never selected
coef(cars.gb_centered)               # intercept implicitly estimated
# and thus returned
## intercept is internally corrected for mean-centering
- mean(cars$speed) * coef(cars.gb_centered, which="speed") # = intercept # not asked for intercept thus not returned coef(cars.gb_centered, which="speed") # explicitly asked for intercept coef(cars.gb_centered, which=c("Intercept", "speed")) ### enhance or restrict model cars.gb <- gamboost(dist ~ speed, data = cars, control = boost_control(mstop = 100, trace = TRUE)) cars.gb[10] cars.gb[100, return = FALSE] # no refitting required cars.gb[150, return = FALSE] # only iterations 101 to 150 # are newly fitted ### coefficients for optimal number of boosting iterations coef(cars.gb[mstop(aic)]) plot(cars$dist, predict(cars.gb[mstop(aic)]),
ylim = range(cars$dist)) abline(a = 0, b = 1) ### example for extraction of coefficients set.seed(1907) n <- 100 x1 <- rnorm(n) x2 <- rnorm(n) x3 <- rnorm(n) x4 <- rnorm(n) int <- rep(1, n) y <- 3 * x1^2 - 0.5 * x2 + rnorm(n, sd = 0.1) data <- data.frame(y = y, int = int, x1 = x1, x2 = x2, x3 = x3, x4 = x4) model <- gamboost(y ~ bols(int, intercept = FALSE) + bbs(x1, center = TRUE, df = 1) + bols(x1, intercept = FALSE) + bols(x2, intercept = FALSE) + bols(x3, intercept = FALSE) + bols(x4, intercept = FALSE), data = data, control = boost_control(mstop = 500)) coef(model) # standard output (only selected base-learners) coef(model, which = 1:length(variable.names(model))) # all base-learners coef(model, which = "x1") # shows all base-learners for x1 cf1 <- coef(model, which = c(1,3,4), aggregate = "cumsum") tmp <- sapply(cf1, function(x) x) matplot(tmp, type = "l", main = "Coefficient Paths") cf1_all <- coef(model, aggregate = "cumsum") cf1_all <- lapply(cf1_all, function(x) x[, ncol(x)]) # last element ## same as coef(model) cf2 <- coef(model, aggregate = "none") cf2 <- lapply(cf2, rowSums) # same as coef(model) ### example continued for extraction of predictions yhat <- predict(model) # standard prediction; here same as fitted(model) p1 <- predict(model, which = "x1") # marginal effects of x1 orderX <- order(data$x1)
## rowSums needed as p1 is a matrix
plot(data$x1[orderX], rowSums(p1)[orderX], type = "b") ## better: predictions on a equidistant grid new_data <- data.frame(x1 = seq(min(data$x1), max(data$x1), length = 100)) p2 <- predict(model, newdata = new_data, which = "x1") lines(new_data$x1, rowSums(p2), col = "red")

### extraction of model characteristics
extract(model, which = "x1")  # design matrices for x1
extract(model, what = "penalty", which = "x1") # penalty matrices for x1
extract(model, what = "lambda", which = "x1") # df and corresponding lambda for x1
## note that bols(x1, intercept = FALSE) is unpenalized

extract(model, what = "bnames")  ## name of complete base-learner
extract(model, what = "variable.names") ## only variable names
variable.names(model)            ## the same

### extract from base-learners
extract(bbs(x1), what = "design")
extract(bbs(x1), what = "penalty")
## weights and lambda can only be extracted after using dpp
weights <- rep(1, length(x1))
extract(bbs(x1)\$dpp(weights), what = "lambda")
# }

Documentation reproduced from package mboost, version 2.9-1, License: GPL-2

### Community examples

Looks like there are no examples yet.