Variance Of Number Research Articles

The Moduli Space of Twisted Laplacians and Random Matrix Theory

Abstract Rudnick recently proved that the spectral number variance for the Laplacian of a large compact hyperbolic surface converges, in a certain scaling limit and when averaged with respect to the Weil–Petersson measure on moduli space, to the number variance of the Gaussian Orthogonal Ensemble of random matrix theory. In this article we extend Rudnick’s approach to show convergence to the Gaussian Unitary Ensemble for twisted Laplacians that break time-reversal symmetry, and to the Gaussian Symplectic Ensemble for Dirac operators. This addresses a question of Naud, who obtained analogous results for twisted Laplacians on high degree random covers of a fixed compact surface.

Key Factors Driving Physiotherapy Use in Patients with Nonspecific Low Back Pain: Retrospective Clinical Data Analysis

Background/objectives: Understanding the factors that influence physiotherapy (PT) service use among patients with nonspecific lower back pain (LBP) is necessary to optimize treatment strategies, healthcare resource allocation, and the planning of value-based initiatives. We report factors that influence the number of PT visits per episode of care (defined as a referral from a physician) for an LBP population in Saudi Arabia, and compare them with patients experiencing their first and recurrent episodes of LBP. Methods: LBP patients were retrospectively enrolled from a clinical dataset derived from an outpatient PT clinic in Saudi Arabia. The primary outcome variable was the number of PT visits performed per episode of care. Multiple linear regression analysis was performed to examine the relationships between the numbers of PT visits per episode of care and independent variables. Results: The number of PT sessions per week (β 0.34, p < 0.001), compliance with PT sessions (β 0.31, p < 0.001), and pre-pain scores (β 0.29, p < 0.001) explained 41.8% (adjusted R2 0.32) of the variance in the total number of PT visits per episode of care (p < 0.001). Conclusions: Factors that might improve value-based care for LBP patients are reported. The more PT sessions per week, compliance with these sessions, and higher baseline pain scores predict a higher number of PT visits per episode of care among these patients. While reported for a Saudi Arabian population, there is no reason to believe that these findings do not apply internationally.

Two-mode subharmonic generating system with coherent and thermal light

The statistical and squeezing characteristics of the light generated by a two-mode subharmonic generating system in a cavity pumped by two-mode coherent light and coupled to a two-mode thermal reservoir through a single-port mirror have been studied in this study. We construct the c-number Langevin equations linked to the normal ordering using the master equation for the system under discussion, and we establish the correlation characteristics of the noise forces. The mean and variance of the photon number of the cavity light are then determined using the solutions of the resulting differential equations. We have discovered that the cavity light mode’s photon statistics are super-Poissonian because the variance of the photon number is more significant than the mean of the photon number. Additionally, using the same solutions, we were able to extract the antinormally ordered characteristic function, which is used to calculate the Q function. In addition, the photon number distribution for the cavity mode is computed using the Q function. The variance of the plus and minus quadrature of the two-mode cavity light generated by the two-mode subharmonic generating system is also obtained. It is discovered that the cavity mode’s squeezing characteristics are unaffected by the two-mode driving coherent light, however, the thermal light has the effect of decreasing the squeezing of the cavity light and the squeezing takes place in the plus quadrature. Finally, we discovered that when the cavity is coupled to a vacuum reservoir, there is a 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} maximum squeezing of the two-mode cavity at a steady state and at the threshold. The nondegenerate subharmonic generator generates a two-mode cavity light that is 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} entangled.

Estimating effective population size using close‐kin mark–recapture

Abstract Close‐kin mark–recapture (CKMR) is a method that allows estimating population census size, among other parameters, through the observed number of pairs that are close‐kin including parent–offspring pairs (POPs) and half‐sibling pairs (HSPs). CKMR models are capable of estimating abundance, fecundity and survival at age using POPs and HSPs from different cohorts. The link between effective population size (Ne) and the number of ‘within‐cohort’ sibling pairs has been noted before but how to actually achieve such an estimate with CKMR has not been previously demonstrated. We show it is possible to use the number of ‘within‐cohort’ sibling pairs along with POPs and ‘different‐cohort’ HSPs to estimate Ne. These can be combined with an estimate of annual variance in number of offspring to estimate the lifetime variance of total reproductive success which can be used to find Ne. We show that the variance in number of offspring produced by adults in a given year is related to the within‐cohort comparisons. Our approach is demonstrated on an individual‐based simulation where we show that the CKMR Ne estimate offers similar results to Ne estimated from methods like linkage disequilibrium. Our methods allow estimating Ne using CKMR while also estimating demographic parameters.

Local order metrics for many-particle systems across length scales

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato , ] to devise even more sensitive order metrics. Published by the American Physical Society 2024

Valsalva maneuver pressure recovery time is prolonged following spinal cord injury with correlations to autonomically-influenced secondary complications.

This work's purpose was to quantify rapid sympathetic activation in individuals with spinal cord injury (SCI), and to identify associated correlations with symptoms of orthostatic hypotension and common autonomically mediated secondary medical complications. This work was a cross-sectional study of individuals with SCI and uninjured individuals. Symptoms of orthostatic hypotension were recorded using the Composite Autonomic Symptom Score (COMPASS)-31 and Autonomic Dysfunction following SCI (ADFSCI) survey. Histories of secondary complications of SCI were gathered. Rapid sympathetic activation was assessed using pressure recovery time of Valsalva maneuver. Stepwise multiple linear regression models identified contributions to secondary medical complication burden. In total, 48 individuals (24 with SCI, 24 uninjured) underwent testing, with symptoms of orthostatic hypotension higher in those with SCI (COMPASS-31, 3.3 versus 0.6, p < 0.01; ADFSCI, 21.2 versus. 3.2, p < 0.01). Pressure recovery time was prolonged after SCI (7.0s versus. 1.7s, p < 0.01), though poorly correlated with orthostatic symptom severity. Neurological level of injury after SCI influenced pressure recovery time, with higher injury levels associated with more prolonged time. Stepwise multiple linear regression models identified pressure recovery time as the primary explanation for variance in number of urinary tract infections (34%), histories of hospitalizations (12%), and cumulative secondary medical complication burden (24%). In all conditions except time for bowel program, pressure recovery time outperformed current clinical tools for assessing such risk. SCI is associated with impaired rapid sympathetic activation, demonstrated here by prolonged pressure recovery time. Prolonged pressure recovery time after SCI predicts higher risk for autonomically mediated secondary complications, serving as a viable index for more "autonomically complete" injury.

Intermediate spectral statistics of rational triangular quantum billiards.

Triangular billiards whose angles are rational multiples of π are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We perform an extensive numerical study of spectral statistics of eight quantized rational triangles, six belonging to the family of right-angled Veech triangles and two obtuse rational triangles. Large spectral samples of up to one million energy levels were calculated for each triangle, which permits one to determine their spectral statistics with great accuracy. It is demonstrated that they are of the intermediate type, sharing some features with chaotic systems, like level repulsion, and some with integrable systems, like exponential tails of the level spacing distributions. Another distinctive feature of intermediate spectral statistics is a finite value of the level compressibility. The short-range statistics such as the level spacing distributions, and long-range statistics such as the number variance and spectral form factors were analyzed in detail. An excellent agreement between the numerical data and the model of gamma distributions is revealed.

On the number variance of sequences with small additive energy

For a real-valued sequence (xn)n=1∞, denote by SN(ℓ) the number of its first N fractional parts lying in a random interval of size ℓ:=L/N, where L=o(N) as N→∞. We study the variance of SN(ℓ) (the number variance) for sequences of the form xn=αan, where (an)n=1∞ is a sequence of distinct integers. We show that if the additive energy of the sequence (an)n=1∞ is bounded from above by N3−ε/L2 for some ε>0, then for almost all α, the number variance is asymptotic to L (Poissonian number variance). This holds in particular for the sequence xn=αnd,d≥2 whenever L=Nβ with 0≤β<1/2.

Wheat yield and grain-filling characteristics due to cultivar replacement in the Haihe Plain in China.

The Haihe Plain plays an important role in wheat production and food security in China and has experienced continuous cultivar replacement since the 1950s.This study assessed the evolution of the yield and grain-filling characteristics of the main winter wheat cultivars in the Haihe Plain over the last seven decades (1950s to date). Cultivar characterization indicated that the increase in yield was negatively affected by spike number and positively affected by the number of kernels per spike before the 2000s and kernel weight after the 2000s. Field trials were conducted across two ecological zones over two consecutive wheatgrowing seasons. The results showed that genetic gains in grain yield, spike number, and kernel weight during 1955 to 2021 were 0.629%, 0.574%, and 0.332% year-1 on a relative basis or 39.12 kg ha-1, 24,350 hm-2, and 0.15 g year-1 on an absolute basis, respectively. However, the increase in the kernel number per spike was not significant. Moreover, cultivar replacement explained 25.6%, 12.8%, and 37.5% of the total variance in grain yield, spike number, and kernel weight, respectively. In summary, during the initial grain-filling stage, wheat cultivar replacement led to the shortening of grain-filling duration and rapid grain-filling rate. However, a longer active grain-filling duration was produced by prolonged durations of rapid and late grain-filling. Additionally, the experimental year had a greater effect on the kernel number, which explained 53.2% of the total variance. Ultimately, modern wheat cultivars had a greater kernel weight. Although the increase in kernel weight has affected grain yield during cultivar replacements in the Haihe Plain, the potential for further yield increase through kernel weight enhancement alone is limited. Consequently, future breeding efforts and cultivation practices should focus on improving spike traits and canopy architecture to enhance productivity.

Local number fluctuations in ordered and disordered phases of water across temperatures: Higher-order moments and degrees of tetrahedrality.

The isothermal compressibility (i.e., related to the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal under near-ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80-1600K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, which scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, under near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, under non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant, especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length scales could shed light on water's nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies.

Variance of the Infection Number of Heterogeneous Malware Spread in Network

The Susceptible–Infected–Susceptible (SIS) model in complex networks is one of the critical models employed in the modeling of virus spread. The study of the heterogeneous SIS model with a non-homogeneous nodal infection rate in finite-size networks has attracted little attention. Investigating the statistical properties of heterogeneous SIS epidemic dynamics in finite networks is thus intriguing. In this paper, we focus on the measure of variability in the number of infected nodes for the heterogeneous SIS epidemic dynamics in finite-size bipartite graphs and star graphs. Specifically, we investigate the metastable-state variance of the number of infected nodes for the SIS epidemic process in finite-size bipartite graphs and star graphs with heterogeneous nodal infection rates. We employ an extended individual-based mean-field approximation to analyze the heterogeneous SIS epidemic process in finite-size bipartite networks and star graphs. We derive the approximation solutions of the variance of the infected number. We verify the proposed theory by simulations. The proposed theory has the potential to help us better understand the fluctuations of SIS models like epidemic dynamics with a non-homogeneous infection rate.

The Ne/N ratio in applied conservation.

Recent developments within the IUCN and the Convention on Biological Diversity have affirmed the increasingly key role that effective population size (N e) and the effective size: census size ratio (N e/N) play in applied conservation and management of global biodiversity. This paper reviews and synthesizes information regarding the definition of N e and demographic and genetic methods for estimating effective size, census size, and their ratio. Emphasis is on single-generation estimates of contemporary N e/N, which are the most informative for practical applications. It is crucial to clearly define which individuals are included in the census size (N). Defining N as the number of adults alive at a given time facilitates comparisons across species. For a wide range of applications and experimental designs, inbreeding N e is simpler to calculate and interpret than variance N e. Effects of skewed sex ratio are generally modest, so most reductions to N e/N arise from overdispersed (greater-than-Poisson) variance in offspring number (). Even when fecundity changes with age, overdispersed within-age variance generally contributes most to overall , and both random and deterministic (mediated by selection) factors can be important. Most species are age-structured, so it is important to distinguish between effective size per generation (N e) and the effective number of breeders in one season or year (N b). Both N e and N b are important for applied conservation and management. For iteroparous species, a key metric is variance in lifetime reproductive success (), which can be affected by a variety of additional factors, including variation in longevity, skip or intermittent breeding, and persistent individual differences in reproductive success. Additional factors that can be important for some species are also discussed, including mating systems, population structure, sex reversal, reproductive compensation, captive propagation, and delayed maturity.

Analysis of mutation profiles in extranodal NK/T-cell lymphoma: clinical and prognostic correlations.

The molecular pathogenesis of extranodal NK/T-cell lymphoma (NKTCL) remains obscured despite the next-generation sequencing (NGS) studies explored on ever larger cohorts in the last decade. We addressed the highly variable mutation frequencies reported among previous studies with comprehensive amplicon coverage and enhanced sequencing depth to achieve higher genomic resolution for novel genetic discovery and comparative mutational profiling of the oncogenesis of NKTCL. Targeted exome sequencing was conducted to interrogate 415 cancer-related genes in a cohort of 36 patients with NKTCL, and a total of 548 single nucleotide variants (SNVs) and 600 Copy number variances (CNVs) were identified. Recurrent amplification of the MCL1 (67%) and PIM1 (56%) genes was detected in a dominant majority of patients in our cohort. Functional mapping of genetic aberrations revealed that an enrichment of mutations in the JAK-STAT signaling pathway, including the cytokine receptor LIFR (copy number loss) upstream of JAK3, STAT3 (activating SNVs), and downstream effectors of MYC, PIM1 and MCL1 (copy number gains). RNA in situ hybridization showed the significant consistence of MCL1 RNA level and copy number of MCL1 gene. We further correlated molecular and clinical parameters with overall survival (OS) of these patients. When correlations were analyzed by univariate followed by multivariate modelling, only copy number loss of LIFR gene and stage (III-IV) were independent prognostic factors of reduced OS. Our findings identified that novel loss of LIFR gene significantly correlated with the adverse clinical outcome of NKTCL patients and provided therapeutic opportunities for this disease through manipulating LIFR.

Meta-analysis of the effects of VAR on goals scored and home advantage in football

Video assistant referee (VAR) has been introduced to elite football (soccer) to avoid clear and obvious mistakes, especially for goal scoring situations. Some literature has reported on VAR’s impact on the game across particular league competitions. The current study meta-analysed data across two seasons (pre-VAR and post-VAR) from 20 competitions ( n = 9076 matches; men’s domestic leagues and both men’s and women’s international tournaments) to examine the overall impact that VAR initially had on number of goals scored, and the extent of inter-competition heterogeneity. A secondary aim was to determine any VAR-associated reduction in home advantage for goals scored, mean result direction and match closeness. Findings demonstrated that there were no overall statistically significant nor meaningful differences between pre and post-VAR seasons/competitions for total number of goals scored per match. Similarly, there were no VAR-associated reductions in home advantage in terms of goals scored, mean result direction and closeness of match outcome. There was moderate heterogeneity for some comparisons, and VAR lessened inter-competition variance for number of goals scored and match score closeness. Implications of findings are discussed. As the largest VAR-focused study and the first to use meta-analytic approach, the current findings are the most comprehensive and definitive to date.

Universality of spectral fluctuations in open quantum chaotic systems

Quantum chaotic systems with one-dimensional spectra follow spectral correlations of Orthogonal (OE), Unitary (UE), or Symplectic Ensembles (SE) of random matrices depending on their invariance under time reversal and rotation. In this letter, we study the non-Hermitian and non-unitary ensembles based on the symmetry of matrix elements, viz. ensemble of complex symmetric, complex asymmetric (Ginibre), and self-dual matrices of complex quaternions. The eigenvalues for these ensembles lie in the two-dimensional plane. We show that the fluctuation statistics of these ensembles are universal and quantum chaotic systems belonging to OE, UE, and SE in the presence of a dissipative environment show similar spectral fluctuations. The short-range correlations are studied using spacing ratio and spacing distribution. For long-range correlations, unfolding at a non-local scale is crucial. We describe a generic method to unfold the two-dimensional spectra with non-uniform density and evaluate correlations using number variance. We find that both short-range and long-range correlations are universal. We verify our results with the quantum kicked top in a dissipative environment that can be tuned to exhibit symmetries of OE, UE, and SE in its conservative limit.

Relation between biomarkers and suicide attempts in patients with schizophrenia

IntroductionAn increased risk of suicide has been reported by psychiatric patients, including schizophrenia1. Numerous evidence suggests alterations in the grade of pro-inflammatory impact on suicidal behavior2, and this relation has been shown in patients with mood or anxious disorders3,4. However, the grade of inflammation impact suicidal behavior in patients with schizophrenia has hardly been investigated.ObjectivesIdentify peripheral blood biomarkers of suicidal behavior in patients with schizophrenia, including inflammatory and lipid profile parameters.MethodsSecondary analysis of a cross-sectional study. Sample: 254 patients with schizophrenia, aged 18-72. Assessments: ad-hoc demographic and clinical questionnaire, PANSS, CDS, CAINS, PSP. Inflammatory and lipid parameters: C-reactive protein (PCR), interleukin 6 (IL-6); high-density lipoprotein cholesterol (HDL-C), low density lipoprotein cholesterol (LDL-C), total cholesterol (TC), triglyceridaemia (TG). Statistical analysis: Correlations, T Student, U Mann-Withney and lineal regression.ResultsMean age: 40.49 (13.10). Men: 64.2%.No statistically significant differences were found between patients with suicide attempts and those without in any of the inflammatory or lipid parameters (p&gt;0.05). However, differences were found in terms of suicide attempts (yes/no) in the PANSS negative (T=-2.217; p=0.028) and PANSS general psychopathy (T=-4.224; p&lt; 0.001), in depressive symptoms (T =-6.967; p&lt; 0.001), and the MAP subscale of the CAINS (T= -3.741; p&lt;0.001).Among patients with suicide attempts (n=42; 16.52% of the sample) (mean=1.90; sd=1.73; Range:1-7), statistically significant correlations were found with PCR (r=0.309; p=0.046), but not with cytokines and lipid parameters. On the other hand, no correlations were found with age, sex, length of illness, and any of the clinical scales.A multiple linear regression was performed considering the number of suicide attempts as the dependent variable and as independent variables, age, sex, and those that were significant in the bivariate analysis (PCR).A predictive model was found that explains 9.60% of the variance of number of suicide attempts (F = 4.224; p &lt; 0.001). The variable that entered the model was PCR (β= 0.309; p=0.046).ConclusionsThe increase in inflammation (manifested by the elevation of PCR) is related to an increase in the number of suicides. On the contrary, no correlations were found with lipid parameters or interleukins.Disclosure of InterestNone Declared

Photon number resolving detection with a single-photon detector and adaptive storage loop

Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.

A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

Number of intraepithelial lymphocytes and presence of a subepithelial band in normal colonic mucosa differs according to stainings and evaluation method

Chronic watery diarrhea is a frequent symptom. In approximately 10% of the patients, a diagnosis of microscopic colitis (MC) is established. The diagnosis relies on specific, but sometimes subtle, histopathological findings. As the histology of normal intestinal mucosa vary, discriminating subtle features of MC from normal tissue can be challenging and therefore auxiliary stainings are increasingly used. The aim of this study was to determine the variance in number of intraepithelial lymphocytes (IELs) and presence of a subepithelial band in normal ileum and colonic mucosa, according to different stains and digital assessment. Sixty-one patients without diarrhea referred to screening colonoscopy due to a positive feacal blood test and presenting with endoscopically normal mucosa were included. Basic histological features, number of IELs, and thickness of a subepithelial band was manually evaluated and a deep learning-based algorithm was developed to digitally determine the number of IELs in each of the two compartments; surface epithelium and cryptal epithelium, and the density of lymphocytes in the lamina propria compartment. The number of IELs was significantly higher on CD3-stained slides compared with slides stained with hematoxylin-and-eosin (HE) (p<0.001), and even higher numbers were reached using digital analysis. No significant difference between right and left colon in IELs or density of CD3-positive lymphocytes in lamina propria was found. No subepithelial band was present in HE-stained slides while a thin band was visualized on special stains. Conclusively, in this cohort of prospectively collected ileum and colonic biopsies from asymptomatic patients, the range of IELs and detection of a subepithelial collagenous band varied depending on the stain and method used for assessment. As assessment of biopsies from patients with diarrhea constitute a considerable workload in the pathology departments digital image analysis is highly desired. Knowledge provided by the present study highlight important differences that should be considered before introducing this method in the clinic.

Constructing a database of alien plants in the Himalaya to test patterns structuring diversity.

Differences in the number of alien plant species in different locations may reflect climatic and other controls that similarly affect native species and/or propagule pressure accompanied with delayed spread from the point of introduction. We set out to examine these alternatives for Himalayan plants, in a phylogenetic framework. We build a database of alien plant distributions for the Himalaya. Focusing on the well-documented regions of Jammu & Kashmir (west) and Bhutan (east) we compare alien and native species for (1) richness patterns, (2) degree of phylogenetic clustering, (3) the extent to which species-poor regions are subsets of species-rich regions and (4) continental and climatic affinities/source. We document 1470 alien species (at least 600 naturalised), which comprise ~14% of the vascular plants known from the Himalaya. Alien plant species with tropical affinities decline in richness with elevation and species at high elevations form a subset of those at lower elevations, supporting location of introduction as an important driver of alien plant richness patterns. Separately, elevations which are especially rich in native plant species are also rich in alien plant species, suggesting an important role for climate (high productivity) in determining both native and alien richness. We find no support for the proposition that variance in human disturbance or numbers of native species correlate with alien distributions. Results imply an ongoing expansion of alien species from low elevation sources, some of which are highly invasive.