Soft logic and numbers

Moshe Klein    - Ph.D student

Abstract:

Marcelo Dascal (2008) wrote about the mathematician and philosopher Gottfried Wilhelm Leibniz, that as a young researcher he aspired to develop a universal language with a single symbol. Spencer-Brown (1969) fulfilled this vision in his book Laws of Form. As suggested by Dascal, Leibniz converted his first vision into a new one: to discover and develop a mathematical language that will demonstrate a softer logic that will overcome the limitations of the dichotomy of truth and falsehood. Leibniz had an ambitious plan to construct a universal language, which will prevent misunderstandings between people as well as serve as a scientific language that reflects thought. According to Dascal, language is a tool for thinking and influences thinking. Precise formal language, precise expression and thinking, are necessary to reduce the number of errors and increase certainty, thus allowing for the resolution of disputes. However, Dascal argues that Leibniz knew that no rational thinking and no “soft rationality” could be described by a formal computational model of rationality and computational language. In fact, Leibniz wrote in many occasions that the logic of two states is insufficient to grasp the full meaning of reason.

In this work ,we propose to see the Necker cube phenomenon as a basis for the development of a mathematical language in accordance with Leibniz’s vision of soft logic. By the development of a new coordinate system, we make a distinction between -0 and +0. This distinction enables us to present points on the Mobius strip in a natural way.

We established a connection between "Recursive Distinctioning" and soft logic, and use it as a basis for a new computational model. This model has a potential to change the current

computational paradigm.

This work was performed under the supervision of Prof. Oded Maimon.

ההרצאה תתקיים ביום שלישי 14.3.17, בשעה 14:00 בחדר 438, בנין וולפסון הנדסה, הפקולטה להנדסה, אוניברסיטת תל-אביב

Speaker: Max Bluvshtein,

M.Sc. student under the supervision of Dr. Ofer Amrani

Wednesday, March 8^th, 2017 at 15:00

Room 011, Kitot Bldg., Faculty of Engineering

Resource Allocation For LDPC-coded multi-carrier Downlink Channels

Abstract

Various techniques have been proposed to address the problem of resource allocation for multi-carrier communications, i.e. Orthogonal frequency-division multiplexing (OFDM) systems. They can be categorized by the type of criteria they aim at optimizing. These criteria, for the most part, arise either from information-theoretic measures such as channel capacity, or from measures that describe the error performance of a channel, which does not necessarily model the coding being employed.

In this work, we propose an optimization technique that is tailored for low density parity-check (LDPC) coded OFDM systems, by employing the so-called general stability condition introduced by Richardson et. al. ("Design of capacity-approaching irregular low-density parity-check codes"). The latter formulates a necessary condition for the Belief-Propagation (BP) decoder to perfectly decode a received vector with no errors.

We re-formulate the general condition so as to model practical multi-carrier/multi-user systems such as OFDMA and OFDRMA (OFDM with random multiple-access). By doing so, a general framework for resource allocation is laid down and employed herein to optimize the transmitted power based on the characteristics of LDPC-coded systems. Fortunately, a convex optimization problem is obtained, whose closed-form solution is elaborated upon in this work. The proposed optimization technique is utilized for performing power allocation in OFDMA and OFDMRA systems in a way that minimizes the transmitted power while guaranteeing reliable decoding.

To validate this technique, it is compared to information-theoretic methods that aim at optimizing the mutual-information between the transmitter and receiver. It is shown that both provide almost identical performance for all the scenarios addressed in this work.

School of Mechanical Engineering Seminar
Monday, May 15, 2017 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

Bi-stability and multi-stability in structures

Prof. Sefi Givli

Faculty of Mechanical Engineering, Technion -Israel Institute of Technology

A wide range of intriguing mechanical phenomena is related to bi-stability and multi-stability. Examples are the shape memory effect and super-elasticity observed in materials undergoing martensitic phase transformations, the mechanical behavior of nano-pillars under compression, and the saw-tooth pattern observed in single molecule experiments of structural proteins such as titin. All these structures are characterized by a wiggly energy landscape and multiple metastable configurations.

In the past few years, we have developed theoretical models aiming at providing insights into the mechanical behavior of such structures. In this talk I will present some of our findings, with emphasis on consequences of discreteness in structures undergoing discrete phase transformations, such as nano-pillars and unfolding/refolding of proteins, and also mechanical aspects of the continuum-level behavior of structures undergoing remodeling or spatial organization of their composition.

Bio: Dr. Sefi Givli Earned his B.Sc (1994) in the Faculty of Mechanical Engineering at Technion. He then served in the Israeli Air-Force as a field engineer and as a system engineer for the F-15/16 jet engines. He joined again the Faculty of Mechanical Engineering at Technion in 2000 for PhD studies (direct track). He then moved to Caltech for a two-year postdoc with Prof. Kaushik Bhattacharya at the department of Mechanical Engineering, where his research has expanded towards mechanics of micro-scale biological systems. Sefi returned to ME Technion in October 2008, where he serves as Assist. Prof. since then.

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