Topological Incarnations of Electroweak Defects

We propose a criterion to classify hybrid defects occurring in field theoretic models such as the standard electroweak model. This criterion leads us to consider the minimal extension of the electroweak model in which electroweak magnetic monopoles and $Z$-strings are topological. We briefly discuss the cosmology of such defects.Comment: 12 pages + 1 figure; LaTe

Other incarnations of the Gross-Pitaevskii dark soliton

We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. As a consequence of this, the GPE soliton gets related to the magnetic soliton in an easy-plane ferromagnet, where it describes the square of the in-plane magnetization of the system. These relationships are shown to be useful in understanding various characteristics of solitons in these distinct many-body systems

Incarnations of Berthelot's conjecture

In this article we give a survey of the various forms of Berthelot's conjecture and some of the implications between them. By proving some comparison results between pushforwards of overconvergent isocrystals and those of arithmetic $\mathcal{D}$-modules, we manage to deduce some cases of the conjecture from Caro's results on the stability of overcoherence under pushforward via a smooth and proper morphism of varieties. In particular, we show that Ogus' convergent pushforward of an overconvergent $F$-isocrystal under a smooth and projective morphism is overconvergent.Comment: 17 pages. Final version, published in J. Number Theor

Vector Bin Packing with Multiple-Choice

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types, each with its own cost and $D$-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about $\ln D$ times the optimum. For the running time to be polynomial we require $D=O(1)$ and $T=O(\log n)$. This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin

The Benefits of Past-Life Regression and Reincarnation

Reincarnation, or the belief in rebirth, is a fascinating belief that many cultures and different groups of people choose to subscribe to. While it typically accompanies various religions, the idea of reincarnation can be presented in other ways as well, such as regression therapy. Past-life regression therapy involves being hypnotized and recalling previous lives, memories, and information possible through levels of incarnations. Many therapists, psychologists, and even laymen attempt to use past-life regression therapy as a useful tool in overcoming anxieties, fears, dealing with every day concerns, and understanding phenomena. “Maintaining a critical eye but also an open mind. In this way, you can appreciate the astonishing experiences.” (Return to Life 17). Being open-minded to the belief in reincarnation specifically through past-life regression therapy has proved to be beneficial to problem-ridden people allowing them to live more fulfilled and purposeful lives. While there may be skeptics, nonbelievers, and alternative explanations, understanding reincarnation in the form of past-life regressions can be amazingly beneficial, transformative, and meaningful