Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

Mirror symmetry, a three dimensional $$ \mathcal{N} $$ N = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d $$ \mathcal{N} $$ N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

Lifespan Prudence

How should a just government distribute resources like jobs, education and healthcare between age groups? How should it ensure that the rules that govern entitlements and restrictions at different stages of our lives are fair rather than age-biased? This chapter answers these questions starting from Norman Daniels’s account of lifespan prudence. Daniels proposes that the unattractive allegory of a war between young and old could be undercut by the simple realization that we can all benefit from some forms of unequal treatment by age. He asks us to convert the interpersonal question into the intrapersonal question “how would an ideally placed agent behind a veil of ignorance distribute scarce resources between different stages of her own life?” This chapter offers an in-depth critical engagement with the framework and offers two resulting principles of age-group justice: lifespan sufficiency and lifespan efficiency.

One, No One, and One Hundred Thousand: The Paradigm of the Z–R Relationship

The Z–R relationship is a scaling-law formulation, Z = ARb, connecting the radar reflectivity Z to the rain rate R. However, more than 100 Z–R relationships, with different values of the parameters, have been reported in literature. This abundance of relationships is in itself a strong indication that no one “physical” relationship exists, a state of affairs that we find similar to that of the protagonist of Luigi Pirandello’s novel One, No One and One Hundred Thousand. Nevertheless the “elevation” of a simple linear fit in the (logR, logZ) space to the role of “scaling law” is such a widespread tenet in literature that it eclipses the simple realization that the abundance of different intercepts and slopes reflects the inhomogeneous nature of rain, and, in ultimate analysis, the statistical variability existing between the number of drops and drop size distribution. Here, we “eliminate” the contribution of the number of drops by rescaling both reflectivity and rainfall rate to per unit drop variables, (Z, R) → (z, r), so that the remaining variability is due only to the variability of the drop size distribution. We use a worldwide database of disdrometer data to show that for the rescaled variables (z, r) only “one,” albeit approximate, scaling law exists.

Dark energy, H0 and weak gravity conjecture

We point out that the physics at the extreme IR — cosmology — might provide tests of the physics of the extreme UV — the Weak Gravity Conjecture. The current discrepancies in the determination of [Formula: see text] may hint at a modification of [Formula: see text]CDM. An extension which may fit better comprises an early contribution to dark energy which “decays” into relativistic matter. On the other hand, the discourse on WGC to date suggests that fields which support cosmic acceleration may produce relativistic matter after they traverse a [Formula: see text] Planckian distance in field space. We explain how this offers a simple realization of the requisite cosmic phenomenology. Thus, if the resolution of [Formula: see text] discrepancies is really early dark energy that ends with a shower of relativistic matter and the current ideas on WGC are indicative, this may be a rare opportunity to link the two extreme limits of quantum field theory.

Investigation of the Lifetime of Antagonistic Shape Memory Wires With Focus on Accelerated Resetting

The antagonistic setup of shape memory actuators enables a multitude of further applications than designs with only one shape memory element. In these actuators, two opposed shape memory elements work against each other and also ensure mutual resetting. This setup allows easily controlled and powersaving actuators for applications with two end positions such as locks or latches. It not only eliminates mechanical resetting, for example by a spring, but also offers a simple realization of holding the end positions energy-free and thereby conserving the shape memory effect. In order to maximize the potential of this actuator design, the authors investigate the interdependencies between antagonistic wires. This paper focuses on the effect of resetting a previously activated NiTi wire by another, similar antagonistic wire before it cooled down completely. On the one hand, very early resetting can have a negative effect on both the cooling and especially the activated wire. This is mainly noticeable in a shortened lifetime of the actuator elements. On the other hand, applying mechanical strain by activating the opposed wire can accelerate phase transformation within the cooling wire. The authors performed corresponding fatigue tests with different cooling times in the antagonistic setup, in order to narrow down a timeframe for the optimized usability of an antagonistic wire actuator.

Rejection sampling of bipartite graphs with given degree sequence

Let A = (a1, a2, ..., an) be a degree sequence of a simple bipartite graph. We present an algorithm that takes A as input, and outputs a simple bipartite realization of A, without stalling. The running time of the algorithm is ⊝(n1n2), where ni is the number of vertices in the part i of the bipartite graph. Then we couple the generation algorithm with a rejection sampling scheme to generate a simple realization of A uniformly at random. The best algorithm we know is the implicit one due to Bayati, Kim and Saberi (2010) that has a running time of O(mamax), where $m = {1 \over 2}\sum\nolimits_{i = 1}^n {{a_i}} and amax is the maximum of the degrees, but does not sample uniformly. Similarly, the algorithm presented by Chen et al. (2005) does not sample uniformly, but nearly uniformly. The realization of A output by our algorithm may be a start point for the edge-swapping Markov Chains pioneered by Brualdi (1980) and Kannan et al.(1999).

Simulation Study of a Digital Hydraulic Drive for a Knee Joint Exoskeleton

Even though the majority of currently published exoskeletons prototypes employ electrical drives, great opportunities are seen for hydraulic drives. Their main advantages are the unrivalled force and power density, facilitating the low additional masses at the peripheral limb joints, and the simple realization of locking, damping, and recuperation functions. The latter function is feasible with some hydraulic control concepts, like primary or secondary motion control. In this paper a digital cylinder drive is studied for getting up from a crouch. This motion is a sound benchmark to test the ability of the drive for exoskeleton knee joint actuation. Digital cylinders can realize output torques only in steps and the transition between different steps can create jerky motions. In this study the motion quality and the losses are evaluated for a binary stepped digital cylinder with four different chambers.

Minimal composite dynamics versus axion origin of the diphoton excess

ATLAS and CMS observe deviations from the expected background in the diphoton invariant mass searches of new resonances around 750 GeV. We show that a simple realization in terms of a new pseudoscalar state can accommodate the observations. The model leads to further footprints that can be soon observed. The new state can be interpreted both as an axion or as a highly natural composite state arising from minimal models of dynamical electroweak (EW) symmetry breaking. We further show how to disentangle the two scenarios. Beyond the possible explanation of the diphoton excess, the results show that it is possible to directly test and constrain composite dynamics via processes stemming from its distinctive topological sector.