Tropical Limit in Statistical Physics

Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated energy levels, particularly of frustrated systems like spin ice and spin glasses. Tropical free energy is a piecewise linear function of temperature, tropical entropy is a piecewise constant function and the system has energy for which tropical Gibbs' probability has maximum. Properties of systems in the points of jump of entropy are studied. Systems with finite and infinitely many energy levels and phenomena of limiting temperatures are discussed.Comment: 16 pages, 6 figure

Strong replica symmetry in high-dimensional optimal Bayesian inference

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how replica symmetry in the strong sense of concentration of all multioverlaps can be established as a consequence of the Franz-de Sanctis identities; the identities themselves in the current setting are obtained via a novel perturbation coming from exponentially distributed "side-observations" of the signal. Concentration of multioverlaps means that asymptotically the posterior distribution has a particularly simple structure encoded by a random probability measure (or, in the case of binary signal, a non-random probability measure). We believe that such strong control of the model should be key in the study of inference problems with underlying sparse graphical structure (error correcting codes, block models, etc) and, in particular, in the rigorous derivation of replica symmetric formulas for the free energy and mutual information in this context

Computational Hardness of Certifying Bounds on Constrained PCA Problems

Given a random n×n symmetric matrix W drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form x⊤Wx over all vectors x in a constraint set S⊂Rn. For a certain class of normalized constraint sets S we show that, conditional on certain complexity-theoretic assumptions, there is no polynomial-time algorithm certifying a better upper bound than the largest eigenvalue of W. A notable special case included in our results is the hypercube S={±1/n−−√}n, which corresponds to the problem of certifying bounds on the Hamiltonian of the Sherrington-Kirkpatrick spin glass model from statistical physics. Our proof proceeds in two steps. First, we give a reduction from the detection problem in the negatively-spiked Wishart model to the above certification problem. We then give evidence that this Wishart detection problem is computationally hard below the classical spectral threshold, by showing that no low-degree polynomial can (in expectation) distinguish the spiked and unspiked models. This method for identifying computational thresholds was proposed in a sequence of recent works on the sum-of-squares hierarchy, and is believed to be correct for a large class of problems. Our proof can be seen as constructing a distribution over symmetric matrices that appears computationally indistinguishable from the GOE, yet is supported on matrices whose maximum quadratic form over x∈S is much larger than that of a GOE matrix.ISSN:1868-896

Supergay: A Queer Analysis of the CW’s Supergirl

An analysis of queer representation and allusions in superhero narratives has been a subject for debate in the both the queer and feminist fields. Throughout history, many scholars have focused on the storyline of superheroes who have “come out” as part of the LGBTQA+ community in comics and in media. However, my paper addresses how a presumed heterosexual character’s introduction into the community as a superhero can be seen as a direct retelling of a queer “coming out” experience in the CW’s show Supergirl (2015). I will discuss Kara Zor-El Danvers’ “coming out” story as Supergirl, as well as how she interacts in society as an alien in a human dominated world, in order to reveal how this can be seen as a direct parallel of a queer narrative. I will also compare how Supergirl portrays a canon homosexual relationship with how the show specifically depicts Supergirl’s interactions with Lena Luthor through camera angles and acting cues that alludes to a veiled homosexual relationship. I will apply Tom Boellstorf’s essay, The Gay Archipelago, to address Supergirl’s narrative as queer. As well as Susan Bordo’s novel Unbearable Weight, to describe Supergirl not only as a feminist icon, but also how society views her as an ‘other’ figure that confirms her queerness. In conclusion, by closely examining how Kara is portrayed in the show, both as a superhero as well as her interactions with other characters, we can conclude that Kara’s transformation into Supergirl is a queer depiction of the superhero narrative

Glassy nature of the hard phase in inference problems

An algorithmically hard phase was described in a range of inference problems: even if the signal can be reconstructed with a small error from an information theoretic point of view, known algorithms fail unless the noise-to-signal ratio is sufficiently small. This hard phase is typically understood as a metastable branch of the dynamical evolution of message passing algorithms. In this work we study the metastable branch for a prototypical inference problem, the low-rank matrix factorization, that presents a hard phase. We show that for noise-to-signal ratios that are below the information theoretic threshold, the posterior measure is composed of an exponential number of metastable glassy states and we compute their entropy, called the complexity. We show that this glassiness extends even slightly below the algorithmic threshold below which the well-known approximate message passing (AMP) algorithm is able to closely reconstruct the signal. Counter-intuitively, we find that the performance of the AMP algorithm is not improved by taking into account the glassy nature of the hard phase. This result provides further evidence that the hard phase in inference problems is algorithmically impenetrable for some deep computational reasons that remain to be uncovered.Comment: 10 pages, 3 figure

A hauntology of participatory speculation

In this paper I conduct a hauntological analysis of participatory speculation, within the context of a study into understanding the potential for increasing recognition of LGBT+ young people’s experiences of hate crime and hate incidents. Hauntology provides a means to further situate accounts of speculation in Participatory Design by sensitising us to the interplay of the virtual and the actual that enables us to expand our sense of the possible. Through understanding how participatory speculation is shaped by absent presences, this paper contributes to the discussion of post-solutionist practices in PD that foster care and responsibility across multiple sites and forms of participation in the face of issues that resist resolution. I conclude by considering by translating speculation into shared spaces of wonder, Participatory Design can foster ethical commitments that stay with the trouble

Kendrick Lamar’s Collapsing of Hip Hop Realness and Christian Identity

In Danielle S. Macon’s To Pimp a Caterpillar: Hip Hop as Vehicle to Spiritual Liberation through the Decolonization of European Ideology about Kendrick Lamar’s To Pimp a Butterfly, she identifies Kendrick’s three-step process of liberation for African-Americans through spirituality: exhibition, revelation, and community orientation. I seek to place her analysis of Kendrick’s music within the context of Daniel White Hodge’s exploration of the neo-sacred secular in Hip Hop, a theological concept containing three elements: a belief that God is in all things, viewing life as having good and bad elements, and a rejection of religionism as the only way to God. Firstly, I will explore how Kendrick takes on himself the tropes of Hip Hop and African-American Street life, not to promote their virtues but to subvert them. Secondly, framing Kendrick’s presentation of an alternative identity built on his reframing of two Christian theological concepts: imago dei and identity as found in person and work of Jesus. Lastly, the process through which he bridges the gap between life in poor African-American urban spaces and Christianity to reconstruct Hip Hop realness in terms of sincerity and a common humanity, instead of the artificially-created litmus tests of Hip Hop authenticity. These three elements are then oriented in Kendrick’s music as the spiritual processes through which he strives to liberate himself, Compton, and his African-American community

Scientific and personal recollections of Roberto Petronzio

This paper aims to recall some of the main contributions of Roberto Petronzio to physics, with a particular regard to the period we have been working together. His seminal contributions cover an extremely wide range of topics: the foundation of the perturbative approach to QCD, various aspects of weak interaction theory, from basic questions (e.g. the mass of the Higgs) to lattice weak interaction, lattice QCD from the beginning to most recent computations.Comment: 15 pages, 5 figures, talk presented at Lattice 201

The Soft-Spoken Girl

This project is a collection of poetry that celebrates the power of the mujeres fuertes in my life, cultural expectations and prevalent barriers. It is set in the Rio Grande Valley where the unique blend of two cultures, caused much heartache and courage. Each poem in this collection weaves a coming of age story