Quantifying the potential and flux landscapes for nonequilibrium multiverse, a new scenario for time arrow

We propose a new scenario of nonequilibirum multiverse. We quantified the potential landscape and the flux landscape for the multiverse. The potential landscape quantifies the weight of each universe. When the terminal vacuum with zero (flat) or negative cosmological constant (AdS) have a chance to tunnel back to the normal universes with positive cosmological constant (dS) through the bounce suggested by the recent studies, the detailed balance of the populations of the multiverse can be broken. We found that the degree of the detailed balance breaking can be quantified by the underlying average flux and associated flux landscape, which gives arise to the dynamical origin of irreversibility and the time arrow of the multiverse. We also showed that the steady state of the multiverse is maintained by the thermodynamic cost quantified by the entropy production rate which is associated to the flux. This gives arise to thermodynamic origin of time irreversibility. On the other hand, we show that the evolution dynamics of the multiverse is determined by both the potential landscape and flux landscape. While the potential landscape determines the weight of the universes in the multiverse and attracts the multiverse to the steady state basins, the flux landscape provides the cycles or loops associating certain universes together. We show that terminal vacuum universes can have dominant weights or lowest potentials giving arise to a funnel shaped potential landscape, while terminal vacuum universes together with other normal universes including ours can form dominant cycles giving arise to a funnel shaped cycle flux landscape. This indicates that even our universe may not be distinct from others based on the probability measure, it may lie in the dominant cycle(s), leading to higher chance of being found. This may provide an additional way beyond the anthropic principle for identifying our universe.

Tight Approximation for Proportional Approval Voting

In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter. The goal is to find a committee of size k that maximizes the total utility of the voters. In this paper, we study approximability of Thiele rules, which are known to be NP-hard to solve exactly. We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric. The algorithm is relatively simple: first we solve a linear program and then we round a solution by employing a framework called pipage rounding due to Ageev and Sviridenko (2004) and Calinescu et al. (2011). We provide a matching lower bound via a reduction from the Label Cover problem. Moreover, assuming a conjecture called Gap-ETH, we show that better approximation ratio cannot be obtained even in time f(k)*pow(n,o(k)).

DETEKSI UCAPAN ANGKA SATU SAMPAI SEPULUH BAHASA PALEMBANG MENGGUNAKAN MFCC DAN BOBOT DOMINAN

Detecting speech with regional language, one of which is Palembang language, has uniqueness and distinctiveness in accent. Differences in dialects to check how precise and influential the accuracy of using MFCC and dominant weights. This study consists of three stages. The first stage, feature extraction of numerical numbers from one to ten using Mel Frequency Cepstral Coefficient (MFCC). The second stage is the selection of features that will be used as feature tables using the proposed model Normalized Dominant Weight (NBD) with threshold similarity, range, filtering, normalization of weights and dominant weights. The third stage is testing by checking by finding similarities in range, filtering, sequential multiplication and calculation of Suitability of Uniformity Patterns (CTF). The test results of checking MFCC and feature selection with normalization of dominant weights were 70% while without feature selection only 42%. Keywords : extraction, weighting, dominant, normalization, range Abstrak Deteksi ucapan dengan berbahasa daerah salah satunya bahasa Palembang mempunyai keunikan dan kekhasan dalam logat berbahasa. Perbedaan logat bahasa untuk mengecekan seberapa tepat dan berpengaruh terhadap akurasi menggunakan MFCC dan Bobot dominan. Penelitian ini terdiri atas tiga tahap. Tahap pertama, ekstraksi ciri angka bahasa angka satu sampai sepuluh menggunakan Mel Frequency Cepstral Coefficient (MFCC). Tahap kedua adalah pemilihan fitur yang akan dijadikan tabel fitur menggunakan model yang diusulkan Normalisasi Bobot Dominan (NBD) dengan kesamaan threshold, jangkauan, filtering, normalisasi bobot dan bobot dominan. Tahap ketiga adalah pengujian dengan pengecekan dengan cara mencari kesamaan jangkauan, filtering, perkalian sekuensial dan perhitungan Kesesuaian Keseragaman Pola (KKP). Hasil pengujian pengecekan terhadap MFCC dan pemilihan fitur dengan normalisasi bobot dominan sebesar 70% sedangkan tanpa pemilihan fitur hanya sebesar 42%. Kata kunci : ekstraksi, bobot, dominan, normalisasi, jangkauan

Quivers with loops and generalized crystals

In the context of varieties of representations of arbitrary quivers, possibly carrying loops, we define a generalization of Lusztig Lagrangian subvarieties. From the combinatorial study of their irreducible components arises a structure richer than the usual Kashiwara crystals. Along with the geometric study of Nakajima quiver varieties, in the same context, this yields a notion of generalized crystals, coming with a tensor product. As an application, we define the semicanonical basis of the Hopf algebra generalizing quantum groups, which was already equipped with a canonical basis. The irreducible components of the Nakajima varieties provide the family of highest weight crystals associated to dominant weights, as in the classical case.

Stabilizers and orbits of first level vectors in modules for the special linear groups

Under some restrictions on the highest weight, the stabilizers of certain vectors in irreducible modules for the special linear groups with a rational action are determined. We consider infinitesimally irreducible modules whose highest weights have all coefficients at least 2 when expressed as a linear combination of the fundamental dominant weights and vectors whose nonzero weight components have weights that differ from the highest weight by a single simple root. For such vectors and modules a criterion for lying in the same orbit is obtained, and we prove that the stabilizers of vectors from different orbits are not conjugate. The orbit dimensions are also found. Furthermore, we show that these vectors do not lie in the orbit of a highest weight vector and their stabilizers are not conjugate to the stabilizer of such a vector.