Intermittent estimation for finite alphabet finitarily Markovian processes with exponential tails

In this paper, we classify by representativeness the elements of a set of complete genomic sequences of Dengue Virus Type 1 (DENV-1), corresponding to the outbreak in Japan during 2014. The set is coming from four regions: Chiba, Hyogo, Shizuoka and Tokyo. We consider this set as composed of independent samples coming from Markovian processes of finite order and finite alphabet. Under the assumption of the existence of a law that prevails in at least 50% of the samples of the set, we identify the sequences governed by the predominant law (see [1, 2]). The rule of classification is based on a local metric between samples, which tends to zero when we compare sequences of identical law and tends to infinity when comparing sequences with different laws. We found that the order of representativeness, from highest to lowest and according to the origin of the sequences is: Tokyo, Chiba, Hyogo, and Shizuoka. When comparing the Japanese sequences with their contemporaries from Asia, we find that the less representative sequence (from Shizuoka) is positioned in groups considerably far away from that which includes the sequences from the other regions in Japan, this offers evidence to suppose that the outbreak in Japan could be produced by more than one type of DENV-1.

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Non-Markovian processes

Physics Subject Headings (PhySH) ◽

10.29172/25a98813-4461-40e1-97be-e5e2dd8fb570 ◽

2018 ◽

Keyword(s):

Markovian Processes

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Markovian processes

Physics Subject Headings (PhySH) ◽

10.29172/4ee22aaf2d974caf9aa84bcc34577f0b ◽

2018 ◽

Keyword(s):

Markovian Processes

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On Sinaĭ Billiards on Flat Surfaces with Horns

Journal of Statistical Physics ◽

10.1007/s10955-021-02746-w ◽

2021 ◽

Vol 183 (2) ◽

Author(s):

Henk Bruin

Keyword(s):

Exponential Decay ◽

Height Function ◽

Suspension Flow ◽

Limit Laws ◽

Suspension Flows ◽

Flat Surfaces ◽

Exponential Tails ◽

Exponential Decay Of Correlations ◽

Sinai Billiards ◽

Young Towers

AbstractWe show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).

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Low-complexity sparse-aware multiuser detection for large-scale MIMO systems

EURASIP Journal on Wireless Communications and Networking ◽

10.1186/s13638-021-01904-8 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Rong Ran ◽

Hayoung Oh

Keyword(s):

Large Scale ◽

Mimo Systems ◽

Minimum Mean Square Error ◽

Multiple Input Multiple Output ◽

Low Complexity ◽

Finite Alphabet ◽

Multiuser Detectors ◽

Input Multiple Output ◽

Error Detector ◽

Significant Performance

AbstractSparse-aware (SA) detectors have attracted a lot attention due to its significant performance and low-complexity, in particular for large-scale multiple-input multiple-output (MIMO) systems. Similar to the conventional multiuser detectors, the nonlinear or compressive sensing based SA detectors provide the better performance but are not appropriate for the overdetermined multiuser MIMO systems in sense of power and time consumption. The linear SA detector provides a more elegant tradeoff between performance and complexity compared to the nonlinear ones. However, the major limitation of the linear SA detector is that, as the zero-forcing or minimum mean square error detector, it was derived by relaxing the finite-alphabet constraints, and therefore its performance is still sub-optimal. In this paper, we propose a novel SA detector, named single-dimensional search-based SA (SDSB-SA) detector, for overdetermined uplink MIMO systems. The proposed SDSB-SA detector adheres to the finite-alphabet constraints so that it outperforms the conventional linear SA detector, in particular, in high SNR regime. Meanwhile, the proposed detector follows a single-dimensional search manner, so it has a very low computational complexity which is feasible for light-ware Internet of Thing devices for ultra-reliable low-latency communication. Numerical results show that the the proposed SDSB-SA detector provides a relatively better tradeoff between the performance and complexity compared with several existing detectors.

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Algebraic singularities of scattering amplitudes from tropical geometry

Journal of High Energy Physics ◽

10.1007/jhep04(2021)002 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

James Drummond ◽

Jack Foster ◽

Ömer Gürdoğan ◽

Chrysostomos Kalousios

Keyword(s):

Scattering Amplitudes ◽

Natural Language ◽

Tropical Geometry ◽

Cluster Algebras ◽

Finite Alphabet ◽

Square Root ◽

Finite Sets ◽

Yang Mills ◽

Square Roots ◽

Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

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