On Local Testability in the Non-Signaling Setting

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of local-to-global phenomena for non-signaling functions. We prove that low-degree testing in the non-signaling setting is possible, assuming that the locality of the non-signaling function exceeds a threshold. We additionally show that if the locality is below the threshold then the test fails spectacularly, in that there exists a non-signaling function which passes the test with probability 1 and yet is maximally far from being low-degree. Along the way, we present general results about the local testability of linear codes in the non-signaling setting. These include formulating natural definitions that capture the condition that a non-signaling function "belongs" to a given code, and characterizing the sets of local constraints that imply membership in the code. We prove these results by formulating a logical inference system for linear constraints on non-signaling functions that is complete and sound

Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching

The gauge-invariant operators up to dimension six in the low-energy effective field theory below the electroweak scale are classified. There are 70 Hermitian dimension-five and 3631 Hermitian dimension-six operators that conserve baryon and lepton number, as well as $\Delta B= \pm \Delta L = \pm 1$, $\Delta L=\pm 2$, and $\Delta L=\pm 4$ operators. The matching onto these operators from the Standard Model Effective Field Theory (SMEFT) up to order $1/\Lambda^2$ is computed at tree level. SMEFT imposes constraints on the coefficients of the low-energy effective theory, which can be checked experimentally to determine whether the electroweak gauge symmetry is broken by a single fundamental scalar doublet as in SMEFT. Our results, when combined with the one-loop anomalous dimensions of the low-energy theory and the one-loop anomalous dimensions of SMEFT, allow one to compute the low-energy implications of new physics to leading-log accuracy, and combine them consistently with high-energy LHC constraints.Comment: 44 pages, 22 tables; version published in JHE

A method for delineation of bone surfaces in photoacoustic computed tomography of the finger

Photoacoustic imaging of interphalangeal peripheral joints is of interest in the context of using the synovial membrane as a surrogate marker of rheumatoid arthritis. Previous work has shown that ultrasound produced by absorption of light at the epidermis reflects on the bone surfaces within the finger. When the reflected signals are backprojected in the region of interest, artifacts are produced, confounding interpretation of the images. In this work, we present an approach where the photoacoustic signals known to originate from the epidermis, are treated as virtual ultrasound transmitters, and a separate reconstruction is performed as in ultrasound reflection imaging. This allows us to identify the bone surfaces. Further, the identification of the joint space is important as this provides a landmark to localize a region-of-interest in seeking the inflamed synovial membrane. The ability to delineate bone surfaces allows us not only to identify the artifacts, but also to identify the interphalangeal joint space without recourse to new US hardware or a new measurement. We test the approach on phantoms and on a healthy human finger

The Renormalization Group Improvement of the QCD Static Potentials

We resum the leading ultrasoft logs of the singlet and octet static QCD potentials within potential NRQCD. We then obtain the complete three-loop renormalization group improvement of the singlet QCD static potential. The discrepancies between the perturbative evaluation and the lattice results at short distances are slightly reduced.Comment: 9 pages, LaTeX, 1 figure. Journal version. Minor changes in the tex

Non-Perturbative Effects in μ→eγ\mu \to e \gamma

We compute the non-perturbative contribution of semileptonic tensor operators $(\bar q \sigma^{\mu \nu} q)(\bar \ell \sigma_{\mu \nu} \ell)$ to the purely leptonic process $\mu \to e \gamma$ and to the electric and magnetic dipole moments of charged leptons by matching onto chiral perturbation theory at low energies. This matching procedure has been used extensively to study semileptonic and leptonic weak decays of hadrons. In this paper, we apply it to observables that contain no strongly interacting external particles. The non-perturbative contribution to $\mu \to e$ processes is used to extract the best current bound on lepton-flavor-violating semileptonic tensor operators, $\Lambda_\text{BSM} \gtrsim 450$ TeV. We briefly discuss how the same method applies to dark-matter interactions.Comment: 21 pages, 1 figure; version published in JHE

HABIT: Hardware-Assisted Bluetooth-based Infection Tracking

The ongoing COVID-19 pandemic has caused health organizations to consider using digital contact tracing to help monitor and contain the spread of COVID-19. Due to this urgent need, many different groups have developed secure and private contact tracing phone apps. However, these apps have not been widely deployed, in part because they do not meet the needs of healthcare officials. We present HABIT, a contact tracing system using a wearable hardware device designed specifically with the goals of public health officials in mind. Unlike current approaches, we use a dedicated hardware device instead of a phone app for proximity detection. Our use of a hardware device allows us to substantially improve the accuracy of proximity detection, achieve strong security and privacy guarantees that cannot be compromised by remote attackers, and have a more usable system, while only making our system minimally harder to deploy compared to a phone app in centralized organizations such as hospitals, universities, and companies. The efficacy of our system is currently being evaluated in a pilot study at Yale University in collaboration with the Yale School of Public Health

On Axis-Parallel Tests for Tensor Product Codes

Many low-degree tests examine the input function via its restrictions to random hyperplanes of a certain dimension. Examples include the line-vs-line (Arora, Sudan 2003), plane-vs-plane (Raz, Safra 1997), and cube-vs-cube (Bhangale, Dinur, Livni 2017) tests. In this paper we study tests that only consider restrictions along axis-parallel hyperplanes, which have been studied by Polishchuk and Spielman (1994) and Ben-Sasson and Sudan (2006). While such tests are necessarily "weaker", they work for a more general class of codes, namely tensor product codes. Moreover, axis-parallel tests play a key role in constructing LTCs with inverse polylogarithmic rate and short PCPs (Polishchuk, Spielman 1994; Ben-Sasson, Sudan 2008; Meir 2010). We present two results on axis-parallel tests. (1) Bivariate low-degree testing with low-agreement. We prove an analogue of the Bivariate Low-Degree Testing Theorem of Polishchuk and Spielman in the low-agreement regime, albeit with much larger field size. Namely, for the 2-wise tensor product of the Reed-Solomon code, we prove that for sufficiently large fields, the 2-query variant of the axis-parallel line test (row-vs-column test) works for arbitrarily small agreement. Prior analyses of axis-parallel tests assumed high agreement, and no results for such tests in the low-agreement regime were known. Our proof technique deviates significantly from that of Polishchuk and Spielman, which relies on algebraic methods such as Bezout\u27s Theorem, and instead leverages a fundamental result in extremal graph theory by Kovari, Sos, and Turan. To our knowledge, this is the first time this result is used in the context of low-degree testing. (2) Improved robustness for tensor product codes. Robustness is a strengthening of local testability that underlies many applications. We prove that the axis-parallel hyperplane test for the m-wise tensor product of a linear code with block length n and distance d is Omega(d^m/n^m)-robust. This improves on a theorem of Viderman (2012) by a factor of 1/poly(m). While the improvement is not large, we believe that our proof is a notable simplification compared to prior work

Initial results of finger imaging using Photoacoustic Computed Tomography

We present a photoacoustic computed tomography investigation on a healthy human finger, to image blood vessels with a focus on vascularity across the interphalangeal joints. The cross-sectional images were acquired using an imager specifically developed for this purpose. The images show rich detail of the digital blood vessels with diameters between 100 $\mu$m and 1.5 mm in various orientations and at various depths. Different vascular layers in the skin including the subpapillary plexus could also be visualized. Acoustic reflections on the finger bone of photoacoustic signals from skin were visible in sequential slice images along the finger except at the location of the joint gaps. Not unexpectedly, the healthy synovial membrane at the joint gaps was not detected due to its small size and normal vascularization. Future research will concentrate on studying digits afflicted with rheumatoid arthritis to detect the inflamed synovium with its heightened vascularization, whose characteristics are potential markers for disease activity.Comment: 2 figure

Testing Linearity against Non-Signaling Strategies

Non-signaling strategies are collections of distributions with certain non-local correlations. They have been studied in Physics as a strict generalization of quantum strategies to understand the power and limitations of Nature\u27s apparent non-locality. Recently, they have received attention in Theoretical Computer Science due to connections to Complexity and Cryptography. We initiate the study of Property Testing against non-signaling strategies, focusing first on the classical problem of linearity testing (Blum, Luby, and Rubinfeld; JCSS 1993). We prove that any non-signaling strategy that passes the linearity test with high probability must be close to a quasi-distribution over linear functions. Quasi-distributions generalize the notion of probability distributions over global objects (such as functions) by allowing negative probabilities, while at the same time requiring that "local views" follow standard distributions (with non-negative probabilities). Quasi-distributions arise naturally in the study of Quantum Mechanics as a tool to describe various non-local phenomena. Our analysis of the linearity test relies on Fourier analytic techniques applied to quasi-distributions. Along the way, we also establish general equivalences between non-signaling strategies and quasi-distributions, which we believe will provide a useful perspective on the study of Property Testing against non-signaling strategies beyond linearity testing