搜索结果：Patterns (New York, N.Y.)

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schrödinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW patterns in the CNLS system, including double-sector, double-heart, and mixed sector-heart configurations. The main novelty is that each RW pattern contains two distinct regions in which two different fundamental first-order RWs coexist simultaneously, potentially appearing as bright (eye-shaped) versus four-petaled or dark (anti-eye-shaped) forms. These two regions are respectively associated with the simple root structures of two different Adler--Moser polynomials: each region consists of well-separated first-order RWs in one-to-one correspondence with the simple roots of the associated polynomial. In addition, by tuning certain free parameters, the two regions of the RW pattern can be shifted to arbitrary locations in the $ (x,t) $-plane. This flexibility, together with the rich simple-root structures of Adler--Moser polynomials, enables the systematic generation of a much broader family of structured RW patterns in the CNLS equation.

Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as boundary measurements, neglecting the rich information embedded in the patterns themselves. Here we introduce a new research direction that directly leverages physical observables from nature--the amplitude of Turing patterns--to achieve complete parameter identification. We present a framework that uses the spatial amplitude profile of a single pattern to simultaneously recover all system parameters, including wavelength, diffusion constants, and the full nonlinear forms of chemotactic and kinetic coefficient functions. Demonstrated on models of chemotactic bacteria, this amplitude-based approach establishes a biologically grounded, mathematically rigorous paradigm for reverse-engineering pattern formation mechanisms across diverse biological systems.

Seasonal patterns of the incidence, hospital visits, and mortality of ischemic heart disease (IHD) have been widely reported. This study aims to investigate seasonal and periodic patterns of IHD hospitalizations in New York using a novel bootstrap approach, the Variable Bandpass Periodic Block Bootstrap (VBPBB) method. Using a bandpass filter, VBPBB isolates the periodically correlated (PC) component of interest from other PC components and noise before bootstrapping, preserving correlation structures and yielding more precise 95\% confidence intervals than existing periodic bootstrapping methods. We examine weekly, monthly, and annual patterns, along with their harmonic frequencies, in the IHD hospitalization. In addition to the pre-defined frequencies, we also examine the frequencies with the highest amplitudes in the periodogram. By aggregating bootstrap results from statistically significant PC components, a 95\% CI band that preserves multiple periodic correlation structures was obtained. Statistically significant variation was observed for the weekly, annual component, and its 2nd, 3rd, 5th, and 6th harmonics. CI bands obtained from VBPBB were much narrower than those from ex

This study presents a comprehensive statistical analysis of criminal complaint data from the New York City Police Department (NYPD) spanning 47 years (1963-2025) [1]. Using a dataset of 438,556 complaint records, we employed exploratory data analysis (EDA), descriptive statistics, and multiple statistical hypothesis tests to investigate the spatial, temporal, and categorical patterns of urban crimes. Our findings revealed significant associations between crime types and geographic locations, temporal variations in criminal activity, and differences in crime severity across time. The results demonstrate that Brooklyn experiences the highest crime volume, petit-larceny constitutes the most common offense, and criminal activity peaks during the evening hours on weekdays, particularly Fridays. Statistical tests, including chi-square tests, Kruskal-Wallis H-test, and Mann-Whitney U test, confirmed highly significant relationships (p < 0.001) across all examined dimensions, providing evidence-based insights for law enforcement resource allocation and urban safety policy development.

We determine the colored patterns that appear in any $2$-edge coloring of $K_{n,n}$, with $n$ large enough and with sufficient edges in each color. We prove the existence of a positive integer $z_2$ such that any $2$-edge coloring of $K_{n,n}$ with at least $z_2$ edges in each color contains at least one of these patterns. We give a general upper bound for $z_2$ and prove its tightness for some cases. We define the concepts of bipartite $r$-tonality and bipartite omnitonality using the complete bipartite graph as a base graph. We provide a characterization for bipartite $r$-tonal graphs and prove that every tree is bipartite omnitonal. Finally, we define the bipartite balancing number and provide the exact bipartite balancing number for paths and stars.

We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as "generalized patterns" or "dashed patterns"). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilf-equivalence. When vincular patterns $α$ and $β$ are filling-shape-Wilf-equivalent, we prove that the direct sum $α\oplusσ$ is filling-shape-Wilf-equivalent to $β\oplusσ$. We also discover two new pairs of patterns which are filling-shape-Wilf-equivalent: when $α$, $β$, and $σ$ are nonempty consecutive patterns which are Wilf-equivalent, $α\oplusσ$ is filling-shape-Wilf-equivalent to $β\oplusσ$; and for any consecutive pattern $α$, $1\oplusα$ is filling-shape-Wilf-equivalent to $1\ominusα$. These equivalences generalize Wilf-equivalences found by Elizalde and Kitaev. These new equivalences imply many new Wilf-equivalences for vincular patterns

Restaurants are critical venues at which to investigate foodborne illness outbreaks due to shared sourcing, preparation, and distribution of foods. Formal channels to report illness after food consumption, such as 311, New York City's non-emergency municipal service platform, are underutilized. Given this, online social media platforms serve as abundant sources of user-generated content that provide critical insights into the needs of individuals and populations. We extracted restaurant reviews and metadata from Yelp to identify potential outbreaks of foodborne illness in connection with consuming food from restaurants. Because the prevalence of foodborne illnesses may increase in warmer months as higher temperatures breed more favorable conditions for bacterial growth, we aimed to identify seasonal patterns in foodborne illness reports from 311 and identify seasonal patterns of foodborne illness from Yelp reviews for New York City restaurants using a Hierarchical Sigmoid Attention Network (HSAN). We found no evidence of significant bivariate associations between any variables of interest. Given the inherent limitations of relying solely on user-generated data for public health ins

We examine the impact of New York City's congestion pricing program through automated analysis of traffic camera data. Our computer vision pipeline processes footage from over 900 cameras distributed throughout Manhattan and New York, comparing traffic patterns from November 2024 through the program's implementation in January 2025 until January 2026. We establish baseline traffic patterns and identify systematic changes in vehicle density across the monitored region.

The rapid growth of social media as a news platform has raised significant concerns about the influence and societal impact of biased and unreliable news on these platforms. While much research has explored user engagement with news on platforms like Facebook, most studies have focused on publicly shared posts. This focus leaves an important question unanswered: how representative is the public sphere of Facebook's entire ecosystem? Specifically, how much of the interactions occur in less-public spaces, and do public engagement patterns for different news classes (e.g., reliable vs. unreliable) generalize to the broader Facebook ecosystem? This paper presents the first comprehensive comparison of interaction patterns between Facebook's more public sphere (referred to as public in paper) and the less public sphere (referred to as private). For the analysis, we first collect two complementary datasets: (1) aggregated interaction data for all Facebook posts (public + private) for 19,050 manually labeled news articles (225.3M user interactions), and (2) a subset containing only interactions with public posts (70.4M interactions). Then, through discussions and iterative feedback from th

We extend the notion of an enumeration scheme developed by Zeilberger and Vatter to the case of vincular patterns (also called "generalized patterns" or "dashed patterns"). In particular we provide an algorithm which takes in as input a set $B$ of vincular patterns and search parameters and returns a recurrence (called a "scheme") to compute the number of permutations of length $n$ avoiding $B$ or confirmation that no such scheme exists within the search parameters. We also prove that if $B$ contains only consecutive patterns and patterns of the form $σ_1σ_2 ... σ_{t-1}-σ_t$, then such a scheme must exist and provide the relevant search parameters. The algorithms are implemented in Maple and we provide empirical data on the number of small pattern sets admitting schemes. We make several conjectures on Wilf-classification based on this data. We also outline how to refine schemes to compute the number of $B$-avoiding permutations of length $n$ with $k$ inversions.

We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length n avoiding a single pattern for the patterns 124-3, 134-2, 231-4, 241-3, 132-4, and 142-3. This nearly completes the Wilf-classification of vincular patterns of length 4. As a corollary, these results imply Wilf-equivalences for certain barred patterns of length 5 with a single bar.

We use wireless voice-call and text-message volumes to quantify spatiotemporal communication patterns in the New York Metro area before, during, and after the Virginia earthquake and Hurricane Irene in 2011. The earthquake produces an instantaneous and pervasive increase in volume and a ~90-minute temporal disruption to both call and text volume patterns, but call volume anomalies are much larger. The magnitude of call volume anomaly diminishes with distance from earthquake epicenter, with multiple clusters of high response in Manhattan. The hurricane produces a two-day, spatially varying disruption to normal call and text volume patterns. In most coastal areas, call volumes dropped anomalously in the afternoon before the hurricane's arrival, but text volumes showed a much less consistent pattern. These spatial patterns suggest partial, but not full, compliance with evacuation orders for low-lying areas. By helping us understand how people behave in actual emergencies, wireless data patterns may assist network operators and emergency planners who want to provide the best possible services to the community. We have been careful to preserve privacy throughout this work by using only

We classify all bi-vincular patterns of length two and three according to the number of permutations avoiding them. These patterns were recently defined by Bousquet-Melou et. al., and are natural generalizations of Babson and Steingrimsson's generalized patterns. The patterns are divided into seven and 24 Wilf classes, for lengths two and three, respectively. For most of the patterns an explicit form for the number of permutations avoiding the pattern is given.

Data mining is the task of discovering interesting patterns from large amounts of data. There are many data mining tasks, such as classification, clustering, association rule mining, and sequential pattern mining. Sequential pattern mining finds sets of data items that occur together frequently in some sequences. Sequential pattern mining, which extracts frequent subsequences from a sequence database, has attracted a great deal of interest during the recent data mining research because it is the basis of many applications, such as: web user analysis, stock trend prediction, DNA sequence analysis, finding language or linguistic patterns from natural language texts, and using the history of symptoms to predict certain kind of disease. The diversity of the applications may not be possible to apply a single sequential pattern model to all these problems. Each application may require a unique model and solution. A number of research projects were established in recent years to develop meaningful sequential pattern models and efficient algorithms for mining these patterns. In this paper, we theoretically provided a brief overview three types of sequential patterns model.

Cities are rarely flat, yet urban network analysis usually represents streets as planar graphs. This simplification affects modeled impedance, route choice, and the interpretation of accessibility, particularly where alternative paths differ in grade. This paper introduces Gridnberg ('grid-n-berg', grid and mountain), a topography-aware pedestrian routing dataset for New York City. The dataset enriches the NYCWalks network with vertex-level elevations derived from the New York City Planimetric Database. For each pedestrian-network geometry vertex, the workflow averages selected elevation observations within a 50 m radius, retains segments with complete vertex support, and uses direction-specific cumulative ascent and descent to calculate three routing costs: horizontal distance, a comfort-oriented slope score, and an accessibility-sensitive slope score. The release retains 313184 of 315577 source segments (99.24%). Gridnberg supports reproducible terrain-aware analysis, transparent scenario comparison, and improved pedestrian-network representations in New York and other cities.

We identify a precise geometric relationship between: (i) certain natural pairs of irreducible reflection groups (``Coxeter pairs"); (ii) self-similar quasicrystalline patterns formed by superposing sets of 1D quasi-periodically-spaced lines, planes or hyper-planes (``Ammann patterns"); and (iii) the tilings dual to these patterns (``Penrose-like tilings"). We use this relationship to obtain all irreducible Ammann patterns and their dual Penrose-like tilings, along with their key properties in a simple, systematic and unified way, expanding the number of known examples from four to infinity. For each symmetry, we identify the minimal Ammann patterns (those composed of the fewest 1d quasiperiodic sets) and construct the associated Penrose-like tilings: 11 in 2D, 9 in 3D and one in 4D. These include the original Penrose tiling, the four other previously known Penrose-like tilings, and sixteen that are new. We also complete the enumeration of the quasicrystallographic space groups corresponding to the irreducible non-crystallographic reflection groups, by showing that there is a unique such space group in 4D (with nothing beyond 4D).

An occurrence of a classical pattern p in a permutation πis a subsequence of πwhose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be required to be adjacent in the permutation. Subsets of permutations characterized by the avoidance--or the prescribed number of occurrences--of generalized patterns exhibit connections to an enormous variety of other combinatorial structures, some of them apparently deep. We give a short overview of the state of the art for generalized patterns.

Security patterns are a means to encapsulate and communicate proven security solutions. They are well-established approaches for introducing security into the software development process. Our objective is to explore the research efforts on security patterns and discuss the current state of the art. This study will serve as a guideline for researchers, practitioners, and teachers interested in this field. We have conducted a systematic mapping study of relevant literature from 1997 until the end of 2017 and identified 403 relevant papers, 274 of which were selected for analysis based on quality criteria. This study derives a customized research strategy from established systematic approaches in the literature. We have utilized an exhaustive 3-tier search strategy to ensure a high degree of completeness during the study collection and used a test set to evaluate our search. The first 3 research questions address the demographics of security pattern research such as topic classification, trends, and distribution between academia and industry, along with prominent researchers and venues. The next 9 research questions focus on more in-depth analyses such as pattern presentation notatio

Two mesh patterns are coincident if they are avoided by the same set of permutations, and are Wilf-equivalent if they have the same number of avoiders of each length. We provide sufficient conditions for coincidence of mesh patterns, when only permutations also avoiding a longer classical pattern are considered. Using these conditions we completely classify coincidences between families containing a mesh pattern of length 2 and a classical pattern of length 3. Furthermore, we completely Wilf-classify mesh patterns of length 2 inside the class of 231-avoiding permutations.