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We show that every Vaisman manifold with large first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold. Furthermore, its complex structure is left-invariant, the characteristic foliation is regular, and the associated fibration is given by the Albanese map. Under the additional assumption that the LCK rank is $1$, the Vaisman structure is also left-invariant. We further prove that if all basic harmonic $1$-forms have constant length, then the Vaisman manifold with large first Betti number is diffeomorphic to a Kodaira-Thurston manifold and its complex structure is the standard complex structure. Finally, we discuss the relationship of this condition with transverse geometric formality in this setting.
Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as $h$-fixed points for an integer parameter $h$ by Hopkins and Sellers. Here, we consider the sequence of first column hook lengths in the Young diagram of a partition and corresponding fixed hooks. We enumerate these, using both generating function and combinatorial proofs, and find that they match occurrences of part sizes equal to their multiplicity. We establish connections to work of Andrews and Merca on truncations of the pentagonal number theorem and classes of partitions partially characterized by certain minimal excluded parts (mex).
The properties of the first galaxies are shaped in large part by the first generations of stars, which emit high energy radiation and unleash both large amounts of mechanical energy and the first heavy elements when they explode as supernovae. We survey the theory of the formation of the first galaxies in this context, focusing on the results of cosmological simulations to illustrate a number of the key processes that define their properties. We first discuss the evolution of the primordial gas as it is incorporated into the earliest galaxies under the influence of the high energy radiation emitted by the earliest stars; we then turn to consider how the injection of heavy elements by the first supernovae transforms the evolution of the primordial gas and alters the character of the first galaxies. Finally, we discuss the prospects for the detection of the first galaxies by future observational missions, in particular focusing on the possibility that primordial star-forming galaxies may be uncovered.
The first stars to form in the Universe -- the so-called Population III stars -- bring an end to the cosmological Dark Ages, and exert an important influence on the formation of subsequent generations of stars and on the assembly of the first galaxies. Developing an understanding of how and when the first Population III stars formed and what their properties were is an important goal of modern astrophysical research. In this review, I discuss our current understanding of the physical processes involved in the formation of Population III stars. I show how we can identify the mass scale of the first dark matter halos to host Population III star formation, and discuss how gas undergoes gravitational collapse within these halos, eventually reaching protostellar densities. I highlight some of the most important physical processes occurring during this collapse, and indicate the areas where our current understanding remains incomplete. Finally, I discuss in some detail the behaviour of the gas after the formation of the first Population III protostar. I discuss both the conventional picture, where the gas does not undergo further fragmentation and the final stellar mass is set by the int
We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems based on calculi of two families: goal-oriented such as model elimination and the connection method, and bottom-up such as the hypertableau calculus. We present the first interpolation method for first-order proofs represented by closed tableaux that proceeds in two stages, similar to known interpolation methods for resolution proofs. The first stage is an induction on the tableau structure, which is sufficient to compute propositional interpolants. We show that this can linearly simulate different prominent propositional interpolation methods that operate by an induction on a resolution deduction tree. In the second stage, interpolant lifting, quantified variables that replace certain terms (constants and compound terms) by variables are introduced. We justify the correctness of interpolant lifting (for the case without built-in equality) abstractly on the basis of Herbrand's theorem and for a different characterization of the formulas to be lifted
The COVID-19 pandemic has resulted in school closures and distancing requirements that have disrupted both work and family life for many. Concerns exist that these disruptions caused by the pandemic may not have influenced men and women researchers equally. Many medical journals have published papers on the pandemic, which were generated by researchers facing the challenges of these disruptions. Here we report the results of an analysis that compared the gender distribution of authors on 1,893 medical papers related to the pandemic with that on papers published in the same journals in 2019, for papers with first authors and last authors from the United States. Using mixed-effects regression models, we estimated that the proportion of COVID-19 papers with a woman first author was 19% lower than that for papers published in the same journals in 2019, while our comparisons for last authors and overall proportion of women authors per paper were inconclusive. A closer examination suggested that women's representation as first authors of COVID-19 research was particularly low for papers published in March and April 2020. Our findings are consistent with the idea that the research product
The first law of entanglement has been used to obtain the linearized Einstein equations of the holographic dual spacetimes. In the present paper, the first law of entanglement in quasi-topological gravity is explicitly derived by using the Iyer-Wald formalism. In addition, we investigate the extended first law of entanglement for the special case in Quasi-Topological gravity.
We discuss the results of recent 3D simulations of first structure formation in relationship to the formation of the first stars. On the basis of a new, high-resolution AMR simulation (spatial dynamic range = 30,000,000), we conclude that the first stars are likely to be massive.
The emergence of new wearable technologies such as action cameras and smart-glasses has increased the interest of computer vision scientists in the First Person perspective. Nowadays, this field is attracting attention and investments of companies aiming to develop commercial devices with First Person Vision recording capabilities. Due to this interest, an increasing demand of methods to process these videos, possibly in real-time, is expected. Current approaches present a particular combinations of different image features and quantitative methods to accomplish specific objectives like object detection, activity recognition, user machine interaction and so on. This paper summarizes the evolution of the state of the art in First Person Vision video analysis between 1997 and 2014, highlighting, among others, most commonly used features, methods, challenges and opportunities within the field.
Parallel best-first search algorithms such as Hash Distributed A* (HDA*) distribute work among the processes using a global hash function. We analyze the search and communication overheads of state-of-the-art hash-based parallel best-first search algorithms, and show that although Zobrist hashing, the standard hash function used by HDA*, achieves good load balance for many domains, it incurs significant communication overhead since almost all generated nodes are transferred to a different processor than their parents. We propose Abstract Zobrist hashing, a new work distribution method for parallel search which, instead of computing a hash value based on the raw features of a state, uses a feature projection function to generate a set of abstract features which results in a higher locality, resulting in reduced communications overhead. We show that Abstract Zobrist hashing outperforms previous methods on search domains using hand-coded, domain specific feature projection functions. We then propose GRAZHDA*, a graph-partitioning based approach to automatically generating feature projection functions. GRAZHDA* seeks to approximate the partitioning of the actual search space graph by p
The search for the first illuminated astronomical sources in the universe is at the edge of the cosmic frontier. Promising techniques for discovering the first objects and their effects span the electromagnetic spectrum and include gravitational waves. We summarize a workshop on discovering and understanding these sources which was held in May 2005 through the Center for Cosmology at the University of California, Irvine.
We use results of angular clustering measurements in 3000 sq. deg's of the FIRST radio survey to infer information on spatial clustering. Measurements are compared with CDM-model predictions. Clustering of FIRST sources with optical ID's in the APM catalog are also investigated. Finally, we outline a preliminary search for a weak lensing signal in the survey.
I briefly outline recent theoretical developments on the formation of the first massive black holes (MBHs) that may grow into the population of MBHs powering quasars and inhabiting galactic centers today. I also touch upon possible observational tests that may give insights on what the properties of the first MBHs were.
Online meeting tools like Zoom and Google Meet have become central to our professional, educational, and personal lives. This has opened up new opportunities for large scale harassment. In particular, a phenomenon known as zoombombing has emerged, in which aggressors join online meetings with the goal of disrupting them and harassing their participants. In this paper, we conduct the first data-driven analysis of calls for zoombombing attacks on social media. We identify ten popular online meeting tools and extract posts containing meeting invitations to these platforms on a mainstream social network, Twitter, and on a fringe community known for organizing coordinated attacks against online users, 4chan. We then perform manual annotation to identify posts that are calling for zoombombing attacks, and apply thematic analysis to develop a codebook to better characterize the discussion surrounding calls for zoombombing. During the first seven months of 2020, we identify over 200 calls for zoombombing between Twitter and 4chan, and analyze these calls both quantitatively and qualitatively. Our findings indicate that the vast majority of calls for zoombombing are not made by attackers st
How did star formation begin in the universe? Some of the questions addressed at this first meeting on "The First Stars" are summarized here from a theoretical perspective, and some brief comments are made on what we may have learned so far.
Biographical essay at the occasion of the first death anniversary of Manfred Bonitz
We study the utility and limitations of using $k$-uniform hypergraphs $H = ([n], E)$ ($n \ge \mathrm{poly}(k)$) in the context of error reduction for randomized algorithms for decision problems with one- or two-sided error. Our error reduction idea is sampling a uniformly random hyperedge of $H$, and repeating the algorithm $k$ times using the hyperedge vertices as seeds. This is a general paradigm, which captures every pseudorandom method generating $k$ seeds without repetition. We show two results which imply a gap between the typical and the worst-case behavior of using $H$ for error-reduction. First, in the context of one-sided error reduction, if using a random hyperedge of $H$ decreases the error probability from $p$ to $p^k + ε$, then $H$ cannot have too few edges, i.e., $|E| = Ω(n k^{-1} ε^{-1})$. Thus, the number of random bits needed for reducing the error from $p$ to $p^k + ε$ cannot be reduced below $\lg n+\lg(ε^{-1})-\lg k+O(1)$. This is also true for hypergraphs of average uniformity $k$. Our result implies new lower bounds for dispersers and vertex-expanders. Second, if the vertex degrees are reasonably distributed, we show that in a $(1-o(1))$-fraction of the cases,
Mathematicians and computer scientists are increasingly leveraging proof assistants to formalize and check complex proofs, a task that demands substantial expertise. Can we lower the bar by automating the conjecturing of helpful, interesting and novel lemmas? We present the first neuro-symbolic lemma conjecturing tool, LEMMANAID, designed to discover conjectures by drawing analogies between mathematical theories. LEMMANAID uses a fine-tuned LLM to generate lemma templates that describe the shape of a lemma, and symbolic methods to fill in the details. We compare LEMMANAID against the same LLM fine-tuned to generate lemmas directly, as well as a fully symbolic conjecturing method. On test sets from Isabelle's HOL library and Archive of Formal Proofs (AFP), LEMMANAID consistently outperforms both neural and symbolic methods. Using DeepSeek-coder-6.7B as a backend, LEMMANAID discovers 50% (HOL) and 29% (AFP) of the gold standard lemmas, increasing to 55% and 35% when ensembling prompting strategies. In a case study on Octonions, LEMMANAID discovers 79% of the gold standard lemmas, compared to 62% for neural-only and 23% for the state of the art symbolic tool. Furthermore, in a targete
Ben-Sasson, Goldreich and Sudan showed that a binary error correcting code admitting a $2$-query tester cannot be good, i.e., it cannot have both linear distance and positive rate. The same holds when the alphabet is a finite field $\mathbb{F}$, the code is $\mathbb{F}$-linear, and the $2$-query tester is $\mathbb{F}$-linear. We show that those are essentially the only limitations on the existence of good locally testable codes (LTCs). That is, there are good $2$-query LTCs on any alphabet with more than $2$ letters, and good $3$-query LTCs with a binary alphabet. Similarly, there are good $3$-query $\mathbb{F}$-linear LTCs, and for every $\mathbb{F}$-vector space $V$ of dimension greater than $1$, there are good $2$-query LTCs with alphabet $V$ whose tester is $\mathbb{F}$-linear. This completely solves, for every $q\geq 2$ and alphabet (resp. $\mathbb{F}$-vector space) $Σ$, the question of whether there is a good $q$-query LTC (resp. $\mathbb{F}$-LTC) with alphabet $Σ$. Our proof builds on the recent good $2$-query $\mathbb{F}$-LTCs of the first author and Kaufman, by establishing a general method for reducing the alphabet size of a low-query LTC.
Let $k$ be a field and let $G$ be an affine algebraic group over $k$. Call a $G$-torsor weakly versal for a class of $k$-schemes $\cal C$ if it specializes to every $G$-torsor over a scheme in $\cal C$. A recent result of the first author, Reichstein and Williams says that for any $d\geq 0$, there exists a $G$-torsor over a finite type $k$-scheme that is weakly versal for finite type affine $k$-schemes of dimension at most $d$. The first author also observed that if $G$ is unipotent, then $G$ admits a torsor over a finite type $k$-scheme that is weakly versal for all affine $k$-schemes, and that the converse holds if $\operatorname{char} k=0$. In this work, we extend this to all fields, showing that $G$ is unipotent if and only if it admits a $G$-torsor over a quasi-compact base that is weakly versal for all finite type regular affine $k$-schemes. Our proof is characteristic-free and it also gives rise to a quantitative statement: If $G$ is a non-unipotent subgroup of $\mathbf{GL}_n$, then a $G$-torsor over a quasi-projective $k$-scheme of dimension $d$ is not weakly versal for finite type regular affine $k$-schemes of dimension $n(d+1)+2$. This means in particular that every such