Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the variance of a sample scales as a power function of the mean of the sample. We study generalizations of Taylor's law in the context of heavy-tailed distributions with infinite mean and variance. We establish the probabilistic limit and analyze the associated convergence rates. Our results extend the existing literature by relaxing the i.i.d. assumption to accommodate dependence and heterogeneity among the random variables. This generalization enables application to dependent data such as time series and network-structured data. We support the theoretical developments by extensive simulations, and the practical relevance through applications to real network data.

Chapter 3 of S. Lloyd's 1988 Ph.D. thesis, `Black Holes, Demons, and the Loss of Coherence: How complex systems get information and what they do with it,' supervisor Heinz Pagels. Reformulates statistical mechanics in terms of pure states and shows that (a) quantum statistics of typical pure states are very close to the mechanics of statistical mechanical ensembles; (b) if a system is in a typical state with energy E, then the reduced density matrix of a subsystem is very close to a thermal state. (A similar result was derived using Levy's lemma some years later by S. Popescu, A.J. Short, A.Winter, Nature Physics 2, 754-758 (2006).) Pure state quantum statistical mechanics is applied to black holesto show that for typical states of matter insideand outside a black hole, the external state is likely to be thermal. Proposes novel interpretation of probabilities in quantum statistical mechanics. Full thesis available at this http URL This chapter was submitted for publication to Physical Review in 1988 but rejected by one sentence referee report: `There is no physics in this paper.' You be the judge.

Unlike many physical nonequilibrium systems, in biological systems, the coupling to external energy sources is not a fixed parameter but adaptively controlled by the system itself. We do not have theoretical frameworks that allow for such adaptability. As a result, we cannot understand emergent behavior in living systems where structure formation and non-equilibrium drive coevolve. Here, using ecosystems as a model of adaptive systems, we develop a framework of living circuits whose architecture changes adaptively with the energy dissipated in each circuit edge. We find that unlike traditional nonequilibrium systems, living circuits exhibit a phase transition from equilibrium death to a nonequilibrium dissipative state beyond a critical driving potential. This transition emerges through a feedback mechanism that saves the weakest edges by routing dissipation through them, even though the adaptive rule locally rewards the strongest dissipating edges. Despite lacking any global optimization principle, living circuits achieve near-maximal dissipation, with higher drive promoting more complex circuits. Our work establishes ecosystems as paradigmatic examples of living circuits whose structure and dissipation are tuned through local adaptive rules.

The iterative bleaching extends multiplexity (IBEX) Knowledge-Base is a central portal for researchers adopting IBEX and related 2D and 3D immunofluorescence imaging methods. The design of the Knowledge-Base is modeled after efforts in the open-source software community and includes three facets: a development platform (GitHub), static website, and service for data archiving. The Knowledge-Base facilitates the practice of open science throughout the research life cycle by providing validation data for recommended and non-recommended reagents, e.g., primary and secondary antibodies. In addition to reporting negative data, the Knowledge-Base empowers method adoption and evolution by providing a venue for sharing protocols, videos, datasets, software, and publications. A dedicated discussion forum fosters a sense of community among researchers while addressing questions not covered in published manuscripts. Together, scientists from around the world are advancing scientific discovery at a faster pace, reducing wasted time and effort, and instilling greater confidence in the resulting data.

We report on a CDF measurement of the total cross section and rapidity distribution, $d\sigma/dy$, for $q\bar{q}\to \gamma^{*}/Z\to e^{+}e^{-}$ events in the $Z$ boson mass region ($66

A positive integer $n$ is defined to be cyclic if and only if every group of size $n$ is cyclic. Equivalently, $n$ is cyclic if and only if $n$ is relatively prime to the number of positive integers less than $n$ that are relatively prime to $n$. Because every prime number is cyclic, it is natural to ask whether a (proved or conjectured) property of primes extends to cyclic numbers. I review proved or conjectured properties of primes (including some new conjectures about primes) and propose analogous conjectures about cyclic numbers. Using the 28,488,167 cyclic numbers less than $10^8$, I test the conjectures about cyclic numbers and disprove the cyclic analog of the second conjecture about primes of Hardy and Littlewood. Proofs or disproofs of the remaining conjectures are invited.

We investigate maximal gauged supergravity in seven dimensions and some of its solitonic solutions. By focusing on a truncation of the gauged SO(5) R-symmetry group to its U(1)^2 Cartan subgroup, we construct general two charge black holes that are asymptotically anti-de Sitter. We demonstrate that 1- and 2-charge black holes preserve 1/2 and 1/4 of the supersymmetries respectively. Additionally, we examine the odd-dimensional self-duality equation governing the three-form potential transforming as the 5 of SO(5), and provide some insight on the construction of membrane solutions in anti-de Sitter backgrounds.

When our immune system encounters foreign antigens (i.e., from pathogens), the B cells that produce our antibodies undergo a cyclic process of proliferation, mutation, and selection, improving their ability to bind to the specific antigen. Immunologists have recently developed powerful experimental techniques to investigate this process in mouse models. In one such experiment, mice are engineered with a monoclonal B-cell precursor and immunized with a model antigen. B cells are sampled from sacrificed mice after the immune response has progressed, and the mutated genetic loci encoding antibodies are sequenced. This experiment allows parallel replay of antibody evolution, but produces data at only one time point; we are unable to observe the evolutionary trajectories that lead to optimized antibody affinity in each mouse. To address this, we model antibody evolution as a multitype branching process and integrate over unobserved histories conditioned on phylogenetic signal in sequence data, leveraging parallel experimental replays for parameter inference. We infer the functional relationship between B-cell fitness and antigen binding affinity in a Bayesian framework, equipped with an efficient likelihood calculation algorithm and Markov chain Monte Carlo posterior approximation. In a simulation study, we demonstrate that a sigmoidal relationship between fitness and binding affinity can be recovered from realizations of the branching process. We then perform inference for experimental data from 52 replayed B-cell lineages sampled 15 days after immunization, yielding a total of 3,758 sampled B cells. The recovered sigmoidal curve indicates that the fitness of high-affinity B cells is over six times larger than that of low-affinity B cells, with a sharp transition from low to high fitness values as affinity increases.

A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.

The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation oscillations in a real system are usually coupled to environmental noise, which further enriches their dynamics, but makes theoretical analysis of such systems and determination of the equation's parameter values a difficult task. In a companion paper we have proposed an analytic approach to a similar problem for another classical nonlinear model, the bistable Duffing oscillator. Here we extend our techniques to the case of the Van der Pol equation driven by white noise. We analyze the statistics of solutions and propose a method to estimate parameter values from the oscillator's time series. We use experimental data of active oscillations in a biological system to demonstrate how our method applies to real observations and how it can be generalized for more complex models.

We report the results of a search for a narrow resonance in electron-positron events in the invariant mass range of 150-950 GeV/c^2 using 1.3 fb^-1 of ppbar collision data at sqrt(s) = 1.96 TeV collected by the CDF II detector at Fermilab. No significant evidence of such a resonance is observed and we interpret the results to exclude the standard model-like Z' with a mass below 923 GeV/c^2 and the Randall-Sundrum graviton with a mass below 807 GeV/c^2 for k/M_pl=0.1, both at the 95% confidence level. Combining with di-photon data excludes the Randall-Sundrum graviton for masses below 889 GeV/c^2 for k/M_pl=0.1.

Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional state measurements (snapshots) from different biological replicates at different time points, but they cannot access the trajectory of any one cell because measurement destroys the cell. Researchers want to forecast (e.g.) differentiation outcomes from early state measurements of stem cells. Recent Schr\"odinger-bridge (SB) methods are natural for interpolating between snapshots. But past SB papers have not addressed forecasting -- likely since existing methods either (1) reduce to following pre-set reference dynamics (chosen before seeing data) or (2) require the user to choose a fixed, state-independent volatility since they minimize a Kullback-Leibler divergence. Either case can lead to poor forecasting quality. In the present work, we propose a new framework, SnapMMD, that learns dynamics by directly fitting the joint distribution of both state measurements and observation time with a maximum mean discrepancy (MMD) loss. Unlike past work, our method allows us to infer unknown and state-dependent volatilities from the observed data. We show in a variety of real and synthetic experiments that our method delivers accurate forecasts. Moreover, our approach allows us to learn in the presence of incomplete state measurements and yields an $R^2$-style statistic that diagnoses fit. We also find that our method's performance at interpolation (and general velocity-field reconstruction) is at least as good as (and often better than) state-of-the-art in almost all of our experiments.

Nonequilibrium systems with strong parameter fluctuations are challenging to describe with standard Statistical Mechanics techniques. Superstatistics -- that can be seen as statistics of an underlying family of statistical distributions -- has emerged as a tool able to describe these complex systems. This has been successfully applied, for example, to hydrodynamic turbulence, internal convection, and even DNA architecture, but not to macroscopic biological systems. Here we document the occurrence of Superstatistics in the animal world, and reveal the emergence of Log-normal Superstatistics in a living system, when ants in a confined space are exposed to a threat. We use a data-driven superstatistical model to explain both normal and "panic" dynamics, identifying non-Gaussian velocity distributions, time scale separation, and the Log-normal statistics of a stochastic diffusion coefficient. We also reveal distinct behavioral regimes in the ants' collective panic response and how it relates with the individual ant memory and cluster formation. Furthermore, our findings indicate that optical signals or simple antennation are not significant mechanisms for panic transmission. These discoveries provide a foundation for the understanding of the biological origin of Log-normal type diffusion in confined environments.

We study a variety of problems in the spectral theory of automorphic forms using entirely analytic techniques such as Selberg trace formula, asymptotics of Whittaker functions and behavior of heat kernels. Error terms for Weyl's law and an analog of Selberg's eigenvalue conjecture for $SL_3({\bf Z})$ is given. We prove the following: Let $\cal H$ be the homogeneous space associated to the group $PGL_3(\bf R)$. Let $X = \Gamma{\backslash SL_3({\bf Z}})$ and consider the first non-trivial eigenvalue $\lambda_1$ of the Laplacian on $L^2(X)$. Using geometric considerations, we prove the inequality $\lambda_1 > 3pi^2/10> 2.96088.$ Since the continuous spectrum is represented by the band $[1,\infty)$, our bound on $\lambda_{1}$ can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space. Brief comment on relevance of automorphic forms to applications in high energy physics is given.

In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees the local existence of an invariant subspace of the dynamics, known as a center manifold, around such nonhyperbolic fixed points. A growing number of theoretical and experimental studies suggest that some neural systems utilize nonhyperbolic fixed points and corresponding center manifolds to display complex, nonlinear dynamics and to flexibly adapt to wide-ranging sensory input parameters. In this paper, we present a technique to study the statistical properties of high-dimensional, nonhyperbolic dynamical systems with random connectivity and examine which statistical properties determine both the shape of the center manifold and the corresponding reduced dynamics on it. This technique also gives us constraints on the family of center manifold models that could arise from a large-scale random network. We demonstrate this approach on an example network of randomly coupled damped oscillators.

Modern biological techniques enable very dense genetic sampling of unfolding evolutionary histories, and thus frequently sample some genotypes multiple times. This motivates strategies to incorporate genotype abundance information in phylogenetic inference. In this paper, we synthesize a stochastic process model with standard sequence-based phylogenetic optimality, and show that tree estimation is substantially improved by doing so. Our method is validated with extensive simulations and an experimental single-cell lineage tracing study of germinal center B cell receptor affinity maturation.

Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. Yet, the set of tools that can characterize such a weighted cycle-rich architecture in a physically relevant, mathematically compact way is sparse. In order to fill this void, we have developed a new algorithm that rests on an abstraction of the physical `tiling' in the case of a two dimensional network to an effective tiling of an abstract surface in space that the network may be thought to sit in. Generically these abstract surfaces are richer than the flat plane and as a result there are now two families of fundamental units that may aggregate upon cutting weakest links -- the plaquettes of the tiling and the longer `topological' cycles associated with the abstract surface itself. Upon sequential removal of the weakest links, as determined by the edge weight, neighboring plaquettes merge and a tree characterizing this merging process results. The properties of this characteristic tree can provide the physical and topological data required to describe the architecture of the network and to build physical models. The new algorithm can be used for automated phenotypic characterization of any weighted network whose structure is dominated by cycles, such as mammalian vasculature in the organs, the root networks of clonal colonies like quaking aspen, or the force networks in jammed granular matter.

We present a general linear response description of membrane adhesion at rough or chemically structured surfaces. Our method accounts for non-local Van der Waals effects and contains the more approximate (and local) Deryagin approach in a simple limit. Specializing to supported membranes we consider the effects of substrate structure on the membrane adhesion energy and configuration. Adhesion is usually less favorable for rough substrates and the membrane shape tends to follow that of the surface contours. Chemical patterning, however, favors adhesion with the membrane configuration being out of phase with the surface structure. Finally, considering a surface indented with `V'-shaped trenches, we show that our approach is in fair agreement with an exact numerical solution.

While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-2D to 3D chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.