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A patient's digital twin is a computational model that describes the evolution of their health over time. Digital twins have the potential to revolutionize medicine by enabling individual-level computer simulations of human health, which can be used to conduct more efficient clinical trials or to recommend personalized treatment options. Due to the overwhelming complexity of human biology, machine learning approaches that leverage large datasets of historical patients' longitudinal health records to generate patients' digital twins are more tractable than potential mechanistic models. In this manuscript, we describe a neural network architecture that can learn conditional generative models of clinical trajectories, which we call Digital Twin Generators (DTGs), that can create digital twins of individual patients. We show that the same neural network architecture can be trained to generate accurate digital twins for patients across 13 different indications simply by changing the training set and tuning hyperparameters. By introducing a general purpose architecture, we aim to unlock the ability to scale machine learning approaches to larger datasets and across more indications so that a digital twin could be created for any patient in the world.

Clinical trials are critical in advancing medical treatments but often suffer from immense time and financial burden. Advances in statistical methodologies and artificial intelligence (AI) present opportunities to address these inefficiencies. Here we introduce Prognostic Covariate-Adjusted Mixed Models for Repeated Measures (PROCOVA-MMRM) as an advantageous combination of prognostic covariate adjustment (PROCOVA) and Mixed Models for Repeated Measures (MMRM). PROCOVA-MMRM utilizes time-matched prognostic scores generated from AI models to enhance the precision of treatment effect estimators for longitudinal continuous outcomes, enabling reductions in sample size and enrollment times. We first provide a description of the background and implementation of PROCOVA-MMRM, followed by two case study reanalyses where we compare the performance of PROCOVA-MMRM versus the unadjusted MMRM. These reanalyses demonstrate significant improvements in statistical power and precision in clinical indications with unmet medical need, specifically Alzheimer's Disease (AD) and Amyotrophic Lateral Sclerosis (ALS). We also explore the potential for sample size reduction with the prospective implementation of PROCOVA-MMRM, finding that the same or better results could have been achieved with fewer participants in these historical trials if the enhanced precision provided by PROCOVA-MMRM had been prospectively leveraged. We also confirm the robustness of the statistical properties of PROCOVA-MMRM in a variety of realistic simulation scenarios. Altogether, PROCOVA-MMRM represents a rigorous method of incorporating advances in the prediction of time-matched prognostic scores generated by AI into longitudinal analysis, potentially reducing both the cost and time required to bring new treatments to patients while adhering to regulatory standards., Comment: 29 pages, 9 tables

Alzheimer's Disease (AD) is a neurodegenerative disease that affects subjects in a broad range of severity and is assessed in clinical trials with multiple cognitive and functional instruments. As clinical trials in AD increasingly focus on earlier stages of the disease, especially Mild Cognitive Impairment (MCI), the ability to model subject outcomes across the disease spectrum is extremely important. We use unsupervised machine learning models called Conditional Restricted Boltzmann Machines (CRBMs) to create Digital Twins of AD subjects. Digital Twins are simulated clinical records that share baseline data with actual subjects and comprehensively model their outcomes under standard-of-care. The CRBMs are trained on a large set of records from subjects in observational studies and the placebo arms of clinical trials across the AD spectrum. These data exhibit a challenging, but common, patchwork of measured and missing observations across subjects in the dataset, and we present a novel model architecture designed to learn effectively from it. We evaluate performance against a held-out test dataset and show how Digital Twins simultaneously capture the progression of a number of key endpoints in clinical trials across a broad spectrum of disease severity, including MCI and mild-to-moderate AD.

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors, analyze their structure, and present the family of equivariant networks that operate on them. We show that any incidence tensor decomposes into invariant subsets. This decomposition, in turn, leads to a decomposition of the corresponding equivariant linear maps, for which we prove an efficient pooling-and-broadcasting implementation., Comment: Last revised August 10, 2020

We introduce a method to compute one-loop soft functions for exclusive $N$-jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the $N$-jettiness hemisphere decomposition of [Jouttenus 2011] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-$k_T$, XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in $pp \to L + 1$ jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius $R$. We find that the small-$R$ results, including corrections up to $\mathcal{O}(R^2)$, accurately capture the full behavior over a large range of $R$., Comment: 33 pages + appendices, 17 figures, v2: journal version, v3: fixed typo in eq.(4.37)

Standard QCD resummation techniques provide precise predictions for the spectrum and the cumulant of a given observable. The integrated spectrum and the cumulant differ by higher-order terms which, however, can be numerically significant. In this paper we propose a method, which we call the $\sigma\text{-improved}$ scheme, to resolve this issue. It consists of two steps: (i) include higher-order terms in the spectrum to improve the agreement with the cumulant central value, and (ii) employ profile scales that encode correlations between different points to give robust uncertainty estimates for the integrated spectrum. We provide a generic algorithm for determining such profile scales, and show the application to the thrust distribution in $e^+e^-$ collisions at NLL$'$+NLO and NNLL$'$+NNLO., Comment: 8 pages, 8 figures

We apply an orthogonalization procedure on the effective field theory of large scale structure (EFT of LSS) shapes, relevant for the angle-averaged bispectrum and non-Gaussian covariance of the matter power spectrum at one loop. Assuming natural-sized EFT parameters, this identifies a linear combination of EFT shapes - referred to as the principal shape - that gives the dominant contribution for the whole kinematic plane, with subdominant combinations suppressed by a few orders of magnitude. For the covariance, our orthogonal transformation is in excellent agreement with a principal component analysis applied to available data. Additionally we find that, for both observables, the coefficients of the principal shapes are well approximated by the EFT coefficients appearing in the squeezed limit, and are thus measurable from power spectrum response functions. Employing data from N-body simulations for the growth-only response, we measure the single EFT coefficient describing the angle-averaged bispectrum with $\mathcal{O}(10\%)$ precision. These methods of shape orthogonalization and measurement of coefficients from response functions are valuable tools for developing the EFT of LSS framework, and can be applied to more general observables., Comment: 18+10 pages, 5 figures

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporate vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity., Comment: 25+3 pages, 7 figures

We compute the non-Gaussian contribution to the covariance of the matter power spectrum at one-loop order in Standard Perturbation Theory (SPT), and using the framework of the effective field theory (EFT) of large scale structure (LSS). The complete one-loop contributions are evaluated for the first time, including the leading EFT corrections that involve seven independent operators, of which four appear in the power spectrum and bispectrum. We compare the non-Gaussian part of the one-loop covariance computed with both SPT and EFT of LSS to two separate simulations. In one simulation, we find that the one-loop prediction from SPT reproduces the simulation well to $k_i + k_j \sim$ 0.25 h/Mpc, while in the other simulation we find a substantial improvement of EFT of LSS (with one free parameter) over SPT, more than doubling the range of $k$ where the theory accurately reproduces the simulation. The disagreement between these two simulations points to unaccounted for systematics, highlighting the need for improved numerical and analytic understanding of the covariance., Comment: v2 - 10+9 pages, 6 figures; minor changes + data analysis and conclusions updated. Version accepted for publication in PRD

In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of "jets without jets". In this paper, we perform the first analytic studies of fractional jet multiplicity $\tilde{N}_{\rm jet}$ in the context of $e^+e^-$ collisions. We use fixed-order QCD to understand the $\tilde{N}_{\rm jet}$ cross section at order $\alpha_s^2$, and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The $\tilde{N}_{\rm jet}$ observable does not satisfy ordinary soft-collinear factorization, and the $\tilde{N}_{\rm jet}$ cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of $\tilde{N}_{\rm jet}$ at hadron colliders like the LHC., Comment: 45 pages, 11 figures, 2 tables; v2: expanded discussion of non-additivity, v3: journal version

We propose a new method for pileup mitigation by implementing "pileup per particle identification" (PUPPI). For each particle we first define a local shape $\alpha$ which probes the collinear versus soft diffuse structure in the neighborhood of the particle. The former is indicative of particles originating from the hard scatter and the latter of particles originating from pileup interactions. The distribution of $\alpha$ for charged pileup, assumed as a proxy for all pileup, is used on an event-by-event basis to calculate a weight for each particle. The weights describe the degree to which particles are pileup-like and are used to rescale their four-momenta, superseding the need for jet-based corrections. Furthermore, the algorithm flexibly allows combination with other, possibly experimental, probabilistic information associated with particles such as vertexing and timing performance. We demonstrate the algorithm improves over existing methods by looking at jet $p_T$ and jet mass. We also find an improvement on non-jet quantities like missing transverse energy., Comment: v2 - 23 pages, 10 figures; update to JHEP version, minor revisions throughout, results unchanged

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables---jet multiplicity, summed scalar transverse momentum, and missing transverse momentum---have event shape counterparts that are closely correlated with their jet-based cousins. Due to their "local" computational structure, these jet-like event shapes could potentially be used for trigger-level event selection at the LHC. Intriguingly, the jet multiplicity event shape typically takes on non-integer values, highlighting the inherent ambiguity in defining jets. By inverting jet multiplicity, we show how to characterize the transverse momentum of the n-th hardest jet without actually finding the constituents of that jet. Since many physics applications do require knowledge about the jet constituents, we also build a hybrid event shape that incorporates (local) jet clustering information. As a straightforward application of our general technique, we derive an event-shape version of jet trimming, allowing event-wide jet grooming without explicit jet identification. Finally, we briefly mention possible applications of our method for jet substructure studies., Comment: v2 - 31 pages, 18 figures; update to JHEP version, section 3.2 expanded, reference to FastJet contrib updated, results unchanged

These lectures from the TASI 2012 summer school outline the basics of supersymmetry (SUSY) in 3+1 dimensions. Starting from a ground-up development of superspace, we develop all of the tools necessary to construct SUSY lagrangians. While aimed at an introductory level, these lectures incorporate a number of "super-tricks" for SUSY aficionados, including SUSY-covariant derivatives, equations of motion in superspace, background field methods, and non-linear realizations of goldstinos., Comment: 75 pages, 4 figures, 1 table. v2: formatting improved, hyperlinks added, references updated

Using published Higgs search data we investigate whether any evidence supports the possibility that the Higgs may be mixed with other neutral scalars. We combine the positive evidence for the Higgs at 125.5 GeV with search constraints at other masses to explore the viability of two simple models. The first Higgs 'friend' model is simply a neutral scalar mixed with the Higgs. In the second Higgs 'accomplice' model the new scalar has an enhanced coupling to photons due to couplings to additional charged fields. We find that the latter scenario allows improvement in fitting the data by accommodating enhanced diphoton rates and suppression in other channels for a Higgs mass of 125.5 GeV. Small excesses at other masses allow the additional scalar to further improve the fit to the data, particularly if it has mass in the vicinity of 210 GeV. Due to observed event rates at 125.5 GeV and strong limits in high mass Higgs searches, mixing angles greater than pi/4 are typically disfavored at the 95% confidence level, depending on the mass of the scalar., Comment: 11 pages, 4 figures. v2 references added, Higgs data updated

If there are multiple hidden sectors which independently break supersymmetry, then the spectrum will contain multiple goldstini. In this paper, we explore the possibility that the visible sector might also break supersymmetry, giving rise to an additional pseudo-goldstino. By the standard lore, visible sector supersymmetry breaking is phenomenologically excluded by the supertrace sum rule, but this sum rule is relaxed with multiple supersymmetry breaking. However, we find that visible sector supersymmetry breaking is still phenomenologically disfavored, not because of a sum rule, but because the visible sector pseudo-goldstino is generically overproduced in the early universe. A way to avoid this cosmological bound is to ensure that an R symmetry is preserved in the visible sector up to supergravity effects. A key expectation of this R-symmetric case is that the Higgs boson will dominantly decay invisibly at the LHC., Comment: v1 - 27 pages, 13 figures, 1 table; v2 - references added; v3 - expanded discussion of higgs sector, JHEP version