Mamara Soorapanman and Murugan's partner fever in Ulapaguppai

Murugan worship is seen as an ancient form of worship in Tamil land. Ganesha's place in this worship has not continued. The literature also does not give a record about Ganesha worship, so it can be seen that the relationship between Murugan and Ganesha was planned and established. But in the rise of devotional literature, Murugan and Ganesha have been brought to the stage of brotherhood. There is a problem between them because of a single fruit called mango. Murugan gets angry with his parents and goes to Palanimalai to stabilize his existence. According to Puranas, Surapaduman, who was standing as a tree after giving suffering to the gods, fell into two parts and turned one into a roofed peacock and the other into a roofed rooster. Muruga, who had lost the mango to Vinayaka, felled the mango tree itself, for felling Surapaduman who was standing as a mango tree. What is the reason for this? How has Murugan's mental discrimination reacted in this place? This article aims to identify and explain all this in detail

Electroweak baryogenesis in the three-loop neutrino mass model with dark matter

Baryon asymmetry of the Universe is evaluated in the model originally proposed in Phys. Rev. Lett. 102 (2009) 051805, where Majorana masses of neutrinos are generated via three-loop diagrams composed of additional scalar bosons including the dark matter candidate which is odd under an unbroken $Z_2$ symmetry. In order for the model to include multiple CP-violating phases, we do not impose the softly broken $Z_2$ symmetry imposed in the original model to avoid the flavor-changing neutral current at tree level. Instead, for simplicity, we assume the flavor alignment structure in the Yukawa interactions. We also simply assume the alignment structure in the Higgs potential so that the Higgs couplings coincide with those in the SM at tree level. Under these phenomenological simplifications, the model still contains multiple CP-violating phases. By using destructive interferences among them, it is compatible with the stringent constraint from the electric dipole moment measurements to generate the observed baryon asymmetry along with the scenario of electroweak baryogenesis. We show a benchmark scenario which can explain neutrino mass, dark matter and baryon asymmetry of the universe simultaneously and can satisfy all the other available experimental data. Some phenomenological predictions of the model are also discussed.Comment: 45 pages, 4 figures, 2 tables, one figure and appendices added, fixed typo

A sight of trees

ThesisTo even start thinking of photographing landscapes, you need to abandon all the human elements of your everyday life and do some soul searching in nature studding and understand all the patterns and ways so easily overlooked by man. It was late afternoon, I lay down under a tree to gather my thoughts and sort out the day's work. I closed my eyes and when I opened them I saw dead tree branches reaching out to the sun setting in the west. The colours in the sky changed rapidly bringing life to the branches that at first appeared dead. I captured these moments in my mind. To explain the emotion I experienced during these moments will never be captured fully in a photo but I strive to perfect the art of capturing the image I saw and the emotions combined with it. It's very important to me as a landscape photographer not only to photograph the patterns or the designs of nature but to create a scene pleasing to the eye with a definite center of attraction. The ability to sense the changes in nature and to photograph these changes in its springing moment when it's still fresh and unseen by most of the people passing by. When I first started to photograph landscapes and especially trees, I felt a bond between human behaviour and the trees but I could not put my finger on it. Because trees are so bold and overpowering in nature the human looked at it and learned from it without really realizing it. When you start to compare man and a tree you see more than one similarity . Trees most of the time grow upwards reaching out to the sky and clouds. Just like people reaching out to the people around , the known or unknown

A Polynomial time Algorithm for Hamilton Cycle with maximum Degree 3

Based on the famous Rotation-Extension technique, by creating the new concepts and methods: broad cycle, main segment, useful cut and insert, destroying edges for a main segment, main goal Hamilton cycle, depth-first search tree, we develop a polynomial time algorithm for a famous NPC: the Hamilton cycle problem. Thus we proved that NP=P. The key points of this paper are: 1) there are two ways to get a Hamilton cycle in exponential time: a full permutation of n vertices; or, chose n edges from all k edges, and check all possible combinations. The main problem is: how to avoid checking all combinations of n edges from all edges. My algorithm can avoid this. Lemma 1 and lemma 2 are very important. They are the foundation that we always can get a good branch in the depth-first search tree and can get a series of destroying edges (all are bad edges) for this good branch in polynomial time. The extraordinary insights are: destroying edges, a tree contains each main segment at most one time at the same time, and dynamic combinations. The difficult part is to understand how to construct a main segment's series of destroying edges by dynamic combinations (see the proof of lemma 4). The proof logic is: if there is at least on Hamilton cycle in the graph, we always can do useful cut and inserts until a Hamilton cycle is got. The times of useful cut and inserts are polynomial. So if at any step we cannot have a useful cut and insert, this means that there are no Hamilton cycles in the graph.Comment: 49 pages. This time, I add a detailed polynomial time algorithm and proof for 3S

LIMEtree: Interactively Customisable Explanations Based on Local Surrogate Multi-output Regression Trees

Systems based on artificial intelligence and machine learning models should be transparent, in the sense of being capable of explaining their decisions to gain humans' approval and trust. While there are a number of explainability techniques that can be used to this end, many of them are only capable of outputting a single one-size-fits-all explanation that simply cannot address all of the explainees' diverse needs. In this work we introduce a model-agnostic and post-hoc local explainability technique for black-box predictions called LIMEtree, which employs surrogate multi-output regression trees. We validate our algorithm on a deep neural network trained for object detection in images and compare it against Local Interpretable Model-agnostic Explanations (LIME). Our method comes with local fidelity guarantees and can produce a range of diverse explanation types, including contrastive and counterfactual explanations praised in the literature. Some of these explanations can be interactively personalised to create bespoke, meaningful and actionable insights into the model's behaviour. While other methods may give an illusion of customisability by wrapping, otherwise static, explanations in an interactive interface, our explanations are truly interactive, in the sense of allowing the user to "interrogate" a black-box model. LIMEtree can therefore produce consistent explanations on which an interactive exploratory process can be built

Rich Counter-Examples for Temporal-Epistemic Logic Model Checking

Model checking verifies that a model of a system satisfies a given property, and otherwise produces a counter-example explaining the violation. The verified properties are formally expressed in temporal logics. Some temporal logics, such as CTL, are branching: they allow to express facts about the whole computation tree of the model, rather than on each single linear computation. This branching aspect is even more critical when dealing with multi-modal logics, i.e. logics expressing facts about systems with several transition relations. A prominent example is CTLK, a logic that reasons about temporal and epistemic properties of multi-agent systems. In general, model checkers produce linear counter-examples for failed properties, composed of a single computation path of the model. But some branching properties are only poorly and partially explained by a linear counter-example. This paper proposes richer counter-example structures called tree-like annotated counter-examples (TLACEs), for properties in Action-Restricted CTL (ARCTL), an extension of CTL quantifying paths restricted in terms of actions labeling transitions of the model. These counter-examples have a branching structure that supports more complete description of property violations. Elements of these counter-examples are annotated with parts of the property to give a better understanding of their structure. Visualization and browsing of these richer counter-examples become a critical issue, as the number of branches and states can grow exponentially for deeply-nested properties. This paper formally defines the structure of TLACEs, characterizes adequate counter-examples w.r.t. models and failed properties, and gives a generation algorithm for ARCTL properties. It also illustrates the approach with examples in CTLK, using a reduction of CTLK to ARCTL. The proposed approach has been implemented, first by extending the NuSMV model checker to generate and export branching counter-examples, secondly by providing an interactive graphical interface to visualize and browse them.Comment: In Proceedings IWIGP 2012, arXiv:1202.422