arXiv subjects
Publications and source records attributed to Jonathan Cohen.
Let $F$ be a non-archimedean local field of characteristic zero and $(π, V)$ a depth zero, irreducible, supercuspidal representation of $GSp(4, F)$. We calculate the dimensions of the spaces of Klingen-invariant vectors in $V$ of level $\mathfrak{p}^n$ for all $n\geq 0 $.
The ability to learn and predict simple functions is a key aspect of human intelligence. Recent works have started to explore this ability using transformer architectures, however it remains unclear whether this is sufficient to recapitulate the extrapolation abilities of people in this domain. Here, we propose to address this gap by augmenting the transformer architecture with two simple inductive learning biases, that are directly adapted from recent models of abstract reasoning in cognitive science. The results we report demonstrate that these biases are helpful in the context of large neural network models, as well as shed light on the types of inductive learning biases that may contribute to human abilities in extrapolation.
An irredundant cover of a finite group $G$ is a collection of proper subgroups whose union is $G$ and which contains no smaller subcover. We classify finite groups which possess exactly two irredundant covers, thereby initiating an answer to a question of Brodie, who classified finite groups with one irredundant cover.
For a finite group $G$, let $\text{rdim}(G)$ denote the smallest dimension of a faithful, complex linear representation of $G$. It is clear that $\text{rdim}(H)\leq \text{rdim}(G)$ for any subgroup $H$ of $G$. We consider $G$ with the property that $\text{rdim}(H)<\text{rdim}(G)$ whenever $H$ is a proper subgroup of $G$, in particular proving a classification of such groups when $G$ is abelian or $\text{rdim}(G)\leq 3$.
Learning to count is an important example of the broader human capacity for systematic generalization, and the development of counting is often characterized by an inflection point when children rapidly acquire proficiency with the procedures that support this ability. We aimed to model this process by training a reinforcement learning agent to select N items from a binary vector when instructed (known as the give-$N$ task). We found that a memory-augmented modular network architecture based on the recently proposed Emergent Symbol Binding Network (ESBN) exhibited an inflection during learning that resembled human development. This model was also capable of systematic extrapolation outside the range of its training set - for example, trained only to select between 1 and 10 items, it could succeed at selecting 11 to 15 items as long as it could make use of an arbitrary count sequence of at least that length. The close parallels to child development and the capacity for extrapolation suggest that our model could shed light on the emergence of systematicity in humans.
Islanded microgrids powered by renewable energy require costly energy storage systems due to the uncontrollable generators. Energy storage needs are amplified when load and generation are misaligned on hourly, monthly, or seasonal timescales. Diversification of both loads and generation can smooth out such mismatches. The ideal type of battery to smooth out remaining generation deficits will depend on the duration(s) that energy is stored. This study presents a controls co-design approach to design an islanded microgrid, showing the benefit of hybridizing tidal and solar generation and hybridizing lithium-ion and flow battery energy storage. The optimization of the microgrid's levelized cost of energy is initially studied in grid-search slices to understand convexity and smoothness, then a particle swarm optimization is proposed and used to study the sensitivity of the hybrid system configuration to variations in component costs. The study highlights the benefits of controls co-design, the need to model premature battery failure, and the importance of using battery cost models that are applicable across orders of magnitude variations in energy storage durations. The results indicate that such a hybrid microgrid would currently produce energy at five times the cost of diesel generation, but flow battery innovations could bring this closer to only twice the cost while using 100% renewable energy.
Humans understand a set of canonical geometric transformations (such as translation and rotation) that support generalization by being untethered to any specific object. We explore inductive biases that help a neural network model learn these transformations in pixel space in a way that can generalize out-of-domain. Specifically, we find that high training set diversity is sufficient for the extrapolation of translation to unseen shapes and scales, and that an iterative training scheme achieves significant extrapolation of rotation in time.
We suggest a new class of tests for searching for lepton flavor non-universality (LFNU) using ratio observables and based on correlations among the underlying LFNU new physics (NP) effects in several (seemingly independent) di-lepton and single lepton + jet(s) processes. This is demonstrated by studying the effects generated by LFNU 4-Fermi interactions involving 3rd generation quarks. We find that the sensitivity to the scale ($Λ$) of the LFNU 4-Fermi operators significantly improves when the correlations among the various di-lepton +jets and single-lepton + jets processes are used, reaching $Λ\sim {\cal O}(10)$~TeV at the HL-LHC.
We study the impact of contact interactions involving two leptons (electrons or muons) and two $b$-quarks ($b \bar{b} \ell^+ \ell^-$) on the high-mass di-lepton region at the LHC. We consider different selections of $b$-tagged jet multiplicities in the di-lepton final states: inclusive (no selection), 0, 1 and 2 $b$-tagged jets, and show that the single $b$-jet selection significantly improves the sensitivity to New Physics (NP) in the form of the $b \bar{b} \ell^+ \ell^-$ contact term. We obtain a better sensitivity compared to the currently existing searches of NP in the di-lepton inclusive channel. In particular, the expected limits go beyond competitive bounds set by LEP (for electrons) on the scale of NP, $Λ$, by a factor of $1.2-3.1$, depending on the chirality structure of the operator. In addition, the expected limits on $Λ$, set by using a non-resonant LHC di-lepton inclusive search, are expected to be improved by a factor of $1.3-1.4$ for both electrons and muons.
We present a new metric of link cohesion for measuring the strength of edges in complex, highly connected graphs. Link cohesion accounts for local small hop connections and associated node degrees and can be used to support edge scoring and graph simplification. We also present a novel graph density measure to estimate the average cohesion across nodes. Link cohesion and the density measure are employed to demonstrate community detection through graph sparsification by maximizing graph density. Link cohesion is also shown to be loosely correlated with edge betweenness centrality.
We examine new aspects of leptoquark (LQ) phenomenology using effective field theory (EFT). We construct a complete set of leading effective operators involving SU(2) singlets scalar LQ and the SM fields up to dimension six. We show that, while the renormalizable LQ-lepton-quark interaction Lagrangian can address the persistent hints for physics beyond the Standard Model in the B-decays $\bar B \to D^{(*)} τ\barν$, $\bar B \to \bar K \ell^+ \ell^-$ and in the measured anomalous magnetic moment of the muon, the LQ higher dimensional effective operators may lead to new interesting effects associated with lepton number violation. These include the generation of one-loop sub-eV Majorana neutrino masses, mediation of neutrinoless double-$β$ decay and novel LQ collider signals. For the latter, we focus on 3rd generation LQ ($ϕ_3$) in a framework with an approximate $Z_3$ generation symmetry, and show that one class of the dimension five LQ operators may give rise to a striking asymmetric same-charge $ϕ_3 ϕ_3$ pair-production signal, which leads to low background same-sign leptons signals at the LHC. For example, with $M_{ϕ_3} \sim 1$ TeV and a new physics scale of $Λ\sim 5$ TeV, we expect about $5000$ positively charged $τ^+ τ^+$ events via $pp \to ϕ_3 ϕ_3 \to τ^+ τ^+ + 2 \cdot j_b$ ($j_b$=b-jet) at the 13 TeV LHC with an integrated luminosity of 300 fb$^{-1}$. It is interesting to note that, in the LQ EFT framework, the expected same-sign lepton signals have a rate which is several times larger than the QCD LQ-mediated opposite-sign leptons signals, $gg,q \bar q \to ϕ_3 ϕ_3^* \to \ell^+ \ell^- +X$. We also consider the same-sign charged lepton signals in the LQ EFT framework at higher energy hadron colliders such as a 27 TeV HE-LHC and a 100 TeV FCC-hh.
We study the impact of R-parity violating Supersymmetry (RPV SUSY) on the 125 GeV Higgs production and decay modes at the LHC. We assume a heavy SUSY spectrum with multi-TeV squarks and SU(2) scalar singlets as well as the decoupling limit in the SUSY Higgs sector. In this case the lightest CP-even Higgs is SM-like when R-parity is conserved. In contrast, we show that when R-parity violating interactions are added to the SUSY framework, significant deviations may occur in some production and decay channels of the 125 GeV Higgs-like state. Indeed, we assume a single-flavor (mostly third generation) Bilinear RPV (BRPV) interactions, which generate Higgs-sneutrino mixing, lepton-chargino mixing and neutrino-neutralino mixing, and find that notable deviations of ${\cal O}(20-30\%)$ may be expected in the Higgs signal strength observables in some channels, e.g., in $p p \to h \to μ^+ μ^-, τ^+ τ^-$. Moreover, we find that new and detectable signals associated with BRPV Higgs decays to gauginos, $h\rightarrowν_τ\tildeχ_{2}^{0}$ and $h\rightarrowτ^{\pm}χ_{2}^{\mp}$, may also arise in this scenario. These decays yield a typical signature of $h \to τ^\pm \ell^\mp + {\not\!\! E_T}$ ($\ell =e,μ,τ$) that can be much larger than in the SM, and may also be accompanied by an ${\cal O}(20-30\%)$ enhancement in the di-photon signal $pp \to h \to γγ$. We also examine potential interesting signals of Trilinear R-parity violation (TRPV) interactions in the production and decays of the Higgs-sneutrino BRPV mixed state (assuming it is the 125 GeV scalar) and show that, in this case also, large deviations up to ${\cal O}(100\%)$ are expected in e.g., $p p \to h \to μ^+ μ^-, τ^+ τ^-$, which are sensitive to the BRPV$\times$TRPV coupling product.
We consider preoperative prediction of thyroid cancer based on ultra-high-resolution whole-slide cytopathology images. Inspired by how human experts perform diagnosis, our approach first identifies and classifies diagnostic image regions containing informative thyroid cells, which only comprise a tiny fraction of the entire image. These local estimates are then aggregated into a single prediction of thyroid malignancy. Several unique characteristics of thyroid cytopathology guide our deep-learning-based approach. While our method is closely related to multiple-instance learning, it deviates from these methods by using a supervised procedure to extract diagnostically relevant regions. Moreover, we propose to simultaneously predict thyroid malignancy, as well as a diagnostic score assigned by a human expert, which further allows us to devise an improved training strategy. Experimental results show that the proposed algorithm achieves performance comparable to human experts, and demonstrate the potential of using the algorithm for screening and as an assistive tool for the improved diagnosis of indeterminate cases.
One of the fundamental predictions of the Standard Model is Lepton Flavour Universality. Any deviation from this prediction would indicate the existence of physics beyond the Standard Model. Recent LHCb measurements present a pattern of deviations from this prediction in rare B-meson decays. While not yet statistically significant (currently $2.2-2.6 σ$), these measurements show an imbalance in the ratio of B-meson decays to a pair of muons in association with a Kaon and decays to a pair of electrons in association with a Kaon. If the measured deviations are indeed present in nature, new physics may mediate interactions involving a pair of same flavour leptons, a $b$- and an $s$-quark. We present the prospect for a search of new physics in this type of interactions at the LHC, in a process that involves an $s$-quark, and a final state with two leptons and a $b$-jet. The proposed search can improve the sensitivity to new physics in these processes by a factor of four compared to current searches with in the total dataset expected at the LHC.
We suggest that the exclusive Higgs + light (or b)-jet production at the LHC, $pp \to h+j(j_b)$, is a rather sensitive probe of the light-quarks Yukawa couplings and of other forms of new physics (NP) in the Higgs-gluon $hgg$ and quark-gluon $qqg$ interactions. We study the Higgs $p_T$-distribution in $pp \to h+j(j_b) \to γγ+ j(j_b)$, i.e., in $h+j(j_b)$ production followed by the Higgs decay $h \to γγ$, employing the ($p_T$-dependent) signal strength formalism to probe various types of NP which are relevant to these processes and which we parameterize either as scaled Standard Model (SM) couplings (the kappa-framework) and/or through new higher dimensional effective operators (the SMEFT framework). We find that the exclusive $h+j(j_b)$ production at the 13 TeV LHC is sensitive to various NP scenarios, with typical scales ranging from a few TeV to ${\cal O}(10)$ TeV, depending on the flavor, chirality and Lorentz structure of the underlying physics.
Celebrity and fandom have been studied extensively in real life. However, with more and more celebrities using social media, the dynamics of interaction between celebrities and fans has changed. Using data from a set of 57,000 fans for the top followed celebrities on Twitter, we define a wide range of features based on their Twitter activity. Using factor analysis we find the most important factors that underlie fan behavior. Using these factors, we conduct analysis on (i) understanding fan behavior by gender \& age, and (ii) para-social breakup behavior. We find that (i) fandom is a social phenomenon, (ii) female fans are often more devoted and younger fans are more active & social, and (iii) the most devoted fans are more likely to be involved in a para-social breakup. Our findings confirm existing research on para-social interactions. Given the scale of our study and dependence on non-reactive data, our paper opens new avenues for research in para-social interactions.
We explore new physics (NP) effects in Higgs-Vector boson associated production at a future International Linear Collider (ILC) via e+e- -> Zh,Zhh, using effective field theory (EFT) techniques. In particular, we focus on a certain class of dimension 6 operators, which are generated by tree-level exchanges of a new heavy vector field in the underlying theory. These operators induce new contact terms of the form ψψϕDϕ, involving the Standard Model (SM) fermions (ψ), gauge-bosons (D is the covariant derivative) and the SM Higgs field (ϕ). We investigate the high-energy behaviour of these new effective interactions in e+e- -> Zh,Zhh, imposing bounds from electroweak precision measurements, and show that the ILC is an excellent testing ground for probing this type of NP via e+e- -> Zh,Zhh. We also address the validity of the EFT expansion and we study the correlation between the hZ and hhZ signals, which can be utilized in future searches for NP in these channels.
We present a library of efficient implementations of deep learning primitives. Deep learning workloads are computationally intensive, and optimizing their kernels is difficult and time-consuming. As parallel architectures evolve, kernels must be reoptimized, which makes maintaining codebases difficult over time. Similar issues have long been addressed in the HPC community by libraries such as the Basic Linear Algebra Subroutines (BLAS). However, there is no analogous library for deep learning. Without such a library, researchers implementing deep learning workloads on parallel processors must create and optimize their own implementations of the main computational kernels, and this work must be repeated as new parallel processors emerge. To address this problem, we have created a library similar in intent to BLAS, with optimized routines for deep learning workloads. Our implementation contains routines for GPUs, although similarly to the BLAS library, these routines could be implemented for other platforms. The library is easy to integrate into existing frameworks, and provides optimized performance and memory usage. For example, integrating cuDNN into Caffe, a popular framework for convolutional networks, improves performance by 36% on a standard model while also reducing memory consumption.