Proof Of Identity Research Articles

Beyond Göllnitz' Theorem I: A bijective approach

In 2003, Alladi, Andrews and Berkovich proved an identity for partitions where parts occur in eleven colors: four primary colors, six secondary colors, and one quaternary color. Their work answered a longstanding question of how to go beyond a classical theorem of Göllnitz, which uses three primary and three secondary colors. Their main tool was a deep and difficult four parameter q-series identity. In this paper we take a different approach. Instead of adding an eleventh quaternary color, we introduce forbidden patterns and give a bijective proof of a ten-colored partition identity lying beyond Göllnitz' theorem. Using a second bijection, we show that our identity is equivalent to the identity of Alladi, Andrews, and Berkovich. From a combinatorial viewpoint, the use of forbidden patterns is more natural and leads to a simpler formulation. In fact, in Part II of this series we will show how our method can be used to go beyond Göllnitz' theorem to any number of primary colors.

A combinatorial identity with applications to forest graphs

We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications. Two applications to enumeration of forests with closed-form expressions are given.

Uniform, Integral, and Feasible Proofs for the Determinant Identities

Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over GF (2) in Hrubeš-Tzameret [15]. Specifically, we show that the multiplicativity of the determinant function and the Cayley-Hamilton theorem over the integers are provable in the bounded arithmetic theory VNC 2 ; the latter is a first-order theory corresponding to the complexity class NC 2 consisting of problems solvable by uniform families of polynomial-size circuits and O (log 2 n )-depth. This also establishes the existence of uniform polynomial-size propositional proofs operating with NC 2 -circuits of the basic determinant identities over the integers (previous propositional proofs hold only over the two-element field).

Heterogeneous identity trust management method based on risk assessment

The cross-trust domain environment in which heterogeneous identity alliances are located often does not have a completely trusted centralized trust root, and different trust domains and entities also have specific security requirements. In view of the above problems, we believe that trust measurement of cross-domain identities based on risk assessment is an effective method to achieve decentralized proof of user identities in heterogeneous cyberspace. There are various risk assessment models. We choose the more mature attack graph theory in the existing research to apply to the new field of cross-trust domain management of heterogeneous identities. We propose an attribute attack graph evaluation model to evaluate cross-domain identities through risk measurement of attributes. In addition, heterogeneous identity alliances also have architectural risks, especially the risk of decentralized underlying structures. In response to this problem, we identify the risk of the identity alliance infrastructure, and combine the risk assessment and presentation system design to verify the principle.

An ethics-based ‘identity-proof’ of god’s existence. An ontology for philotherapy

A resurgence of scholarly work on proof of God?s existence is noticeable over the past decade, with considerable emphasis on attempts to provide ?analytic proof? based on the meanings and logic of various identity statements which constitute premises of the syllogisms of the ?proof?. Most recently perhaps, Emmanuel Rutten?s ?modal-epistemic proof? has drawn serious academic attention. Like other ?analytic? and strictly logical proofs of God?s existence, Rutten?s proof has been found flawed. In this paper I discuss the possibility of an ?ethics-based? identity proof of God?s existence. Such a proof, the first version of which, I believe, has been offered, indirectly, by Nikolai Lossky, utilizes the form and structure of the analytic proof, but fundamentally rests on the perception of moral values we associate with God and Godliness. The nature of the proof shifts the focus of the very attempt to ?prove? God?s existence from what I believe is an unreasonable standard, unattainable even in ?proving? the existence of the more mundane world, towards a more functional, practical and attainable standard. The proof proposed initially by Lossky, and in a more systematic form here, I believe, shows the indubitable existence of God in the sense of his moral presence in the lives of the faithful, at least with the same degree of certainty as the presence or ?existence? of anything else that can be epistemically proven in principle.

Some aspects of personal identity on the materials of french media

The paper studies the concept of identity verification of the personality in the state system from the perspective of finding additional socially marked meanings/connotations of the word “identity/ identité”. It is also necessary to consider the contexts affecting the variety of meanings that this concept embraces.The study is based on the contexts derived from the French mass media. While describing the concept of identity verification, we use the term “diagnostic markers” to classify the meanings of the lexeme “identity/identité”. These markers can be represented by the linguistic units of different levels, which are used to detect the meaning of identity in a particular information context. The study of the concept helped to detect the associative field of “identity/ identité” from the perspective of personality verification in the state system. Thus, the nuclear meaning is the obligation for a French citizen to carry la carte d’identité/an identity card, while the peripheral meanings include the following: true and false optionality for providing the proof of identity; the contrast between real and official identities; identity as a proof (official document) of one’s nationality; lack of identity in the meaning of absence of legal proof of identity; identity in the context of restrictions imposed as a result of tough immigration policies. The social markers used to identify the personality within the state system were also analyzed from the perspective of ascribed and achieved identity. The first type refers to the situation of actually living in the chosen country, while the second type occurs when a person chooses a country for future residence.

The Sustainable Development Goals and ‘legal identity for all’: ‘First, do no harm’

• The adoption of SDG target 16.9 has brought belated recognition of the importance of a person’s ‘legal identity’. • New ‘legal identity’ systems are being implemented out without sufficient attention to potential negative impacts. • To achieve the desired positive impacts, detailed attention is needed to the regulation of enrolment processes. • To avoid doing harm, independent oversight and reduced state discretion are critical. The right to legal identity, previously neglected by the development community, has gained recognition by the adoption of a target in the SDGs to ‘provide legal identity for all, including birth registration’. In the initial absence of definition of ‘legal identity’ beyond birth registration, different actors have interpreted the target according to their own priorities, whether they be human rights protection, development, national security – or rent-seeking. Long-standing scholarship recognises both the positive and negative potential impacts of state identification systems; the adoption of new biometric technologies strengthens these potential impacts, for good or ill. The importance of data protection and the risks to privacy created by digital technologies are well-recognised. This article returns to arguments made by Simon Szreter in World Development in 2007, to argue the critical importance of independent oversight of executive decisions relating to legal identity; it adds an emphasis on the detailed regulation of enrolment processes, and the importance of nationality law reforms, as government-backed identity schemes are upgraded or introduced. The article argues that the introduction of new ‘foundational’ national identification systems for adults and more pervasive requirements for proof of identity, without simultaneously addressing gaps in the legal framework governing the determination of legal status, risks making the problems around proof of legal identity worse rather than better.

Iot Based Smart Home Security System with Face Recognition and Weapon Detection Using Computer Vision

Today home automation systems are popular in households. The control of electric fixtures like fans and lights is possible with the help of Internet of Things (IOT). The problem arises due to intrusion of burglars. The security of such systems has been done using computer vision and IOT. Here we aim to enhance this system by use of image processing for object detection. The system uses cameras at the door for face recognition as access control. Also, vibration and door magnet sensors are installed at the entry points to detect when the burglar tries to barge inside. PIR sensors are employed to detect human presence. A vibration sensor is also used to give alert if any shock nearby is detected. The system allows entry only if authorized person like owner or person registered on the database arrives. The person may be identified through valid proof of identity. It sends a message to the owner in case it doesn’t recognize the person within 20 seconds and the owner can monitor the activities via live feed from the camera. All sensor signals are checked and status of the system is updated continuously. In case the burglar tries to break inside, siren is activated and alert messages are redirected to the owner and the police.

Hard to reach: COVID-19 responses and the complexities of homelessness

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has caused more than 954 000 deaths worldwide to date,1WHOWorld Health Organization coronavirus disease COVID-19 dashboard.https://covid19.who.int/tableDate accessed: September 21, 2020Google Scholar but the burden of morbidity and mortality has fallen unevenly on particular countries and population groups. Worldwide, COVID-19 has been recognised as a potential public health problem among people experiencing homelessness and other vulnerable cohorts such as prisoners.2Del Brutto OH Mera RM Recalde BY Costa AF Social determinants of health and risk of SARS-CoV-2 infection in community-dwelling older adults living in a rural Latin American setting.J Community Health. 2020; (published online July 15.)https://dx.doi.org/10.1007/s10900-020-00887-9Crossref Scopus (0) Google Scholar, 3Naik SS Gowda GS Shivaprakash P et al.Homeless people with mental illness in India and COVID-19.Lancet Psychiatry. 2020; 7: e51-e52Summary Full Text Full Text PDF PubMed Scopus (0) Google Scholar, 4Oladimeji O Atiba BP Mbokazi JA Hyera FLM The homeless, inmates and refugees in Africa in the face of Covid-19 outbreak.Open Publ Health J. 2020; 13: 306-308Crossref Scopus (0) Google Scholar Broadly, reduced access to health care and basic sanitation, the potential for mobility between services and crowding within facilities, the greater sharing of resources between individuals, substance-seeking behaviours, economic need resulting in employment such as survival sex work,5Watson J Youth homelessness and survival sex: intimate relationships and gendered subjectivities. Routledge, London2017Crossref Google Scholar and underlying health conditions put such individuals theoretically more at risk of morbidity and mortality from COVID-19. There is growing evidence, however, of regional differences in the impact of COVID-19 on the socially vulnerable.6Karaye IM Horney JA The impact of social vulnerability on COVID-19 in the US: an analysis of spatially varying relationships.Am J Prev Med. 2020; 59: 317-325Summary Full Text Full Text PDF PubMed Scopus (0) Google Scholar, 7Maroko AR Nash D Pavilonis BT COVID-19 and inequity: a comparative spatial analysis of New York City and Chicago hot spots.J Urban Health. 2020; 97: 461-470Crossref PubMed Scopus (0) Google Scholar

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.

Detecting a security breach and pinpointing its source

Abstract There are many rapidly emerging technologies to embed a “Root of Trust” (RoT) in silicon or in assembled packages and PCBs further down the supply chain. These all aim to provide an un-hackable proof of device identity and uncompromised firmware. Despite these efforts we can, and should, assume that bad actors will succeed to counterfeit devices, install malware, etc. So how do we detect and respond to these attacks in time before they cause too much harm? This is, of course, of particular concern for defense and aerospace applications. We will discuss an initiative at SEMI to provide asset traceability through the supply chain. The intention is to detect counterfeits and security attacks quickly, track them back through the supply chain and identify the culprit. The threat of capture and penalties is expected to reduce the incentive for the bad actors in future. The proposed SEMI standard will define the transactions and data required to record chain of custody for electronic assets as they flow through the supply chain. These transactions will be recorded on Hyperledger Fabric, a blockchain platform which offers an immutable transaction ledger, maintained within a distributed network of peer nodes. The ledger will not be public (like bitcoin), nor will it be private to one organization. Instead it will follow a consortium model and be permissioned to support flexible trust assumptions. The SEMI standard will facilitate supply chain members to form one or more consortiums and host the Hyperledger nodes. This will enable the early detection and response to counterfeit and security threats to electronic assets that the supply chain members manufacture or distribute. The standard takes care not to expose any confidential technical or commercial information. However, Hyperledger offers the concepts of private data collections and channels to allow for the sharing of private data between specific members. This could become an enabler to realize the data sharing required to meet Smart Manufacturing 4.0 objectives. There are a number of similar chain of custody ledger initiatives underway both in the commercial and standards arena. The hope is that the SEMI standard will encourage these systems to merge into an industry wide consortium with increased interoperability, performance, reliability and security.

Exclusion and inclusion in identification: regulation, displacement and data justice

ABSTRACT Around the world, regimes of identification regulate people’s interactions with state and commercial institutions. These regimes promise access to resources and entitlements, while also facilitating people’s visibility to states and therefore their governability. For many, proving one’s identity presents no challenge; however, it is estimated that a billion people have no official proof of identity. Meanwhile, the humanitarian sector is undergoing a transformation in which digital identity, mobile connectivity and digital finance are central features. Through a data justice lens, this paper explores customer identification regimes in two country contexts in which large displaced populations are present: Uganda and Bangladesh. The two cases reveal divergent approaches to regulating refugee identification: while Uganda's policy environment has recently become more inclusive, Bangladesh's proves to be particularly restrictive. We reflect on what these cases mean for the future development of digital identity systems by the humanitarian sector and the implications for data justice.

Proof for a q-Trigonometric Identity of Gosper

Proof for a q-Trigonometric Identity of Gosper

On the existence of telescopers for rational functions in three variables

Zeilberger's method of creative telescoping is crucial for the computer-generated proofs of combinatorial and special-function identities. Telescopers are linear differential or (q-)recurrence operators computed by algorithms for creative telescoping. Two fundamental problems related to creative telescoping are whether telescopers exist, and how to construct them efficiently when they do. In this paper, we solve the existence problem of telescopers for rational functions in three variables including 18 cases. We reduce the existence problem from the trivariate case to the bivariate case and some related problems. The existence criteria given in this paper enable us to determine the termination of algorithms for creative telescoping with trivariate rational inputs.

An Identity from Viète

SummaryWe provide a visual proof for a sine identity used by Viète in the computation of his sine table. The figure also proves the counterpart for the cosine function.

Tau functions of the charged free bosons

We study bosonic tau functions in relation with the charged free bosonic fields. It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector, and some tau functions were given in the completion of M using Schur functions. We also give a new proof of Borchardt's identity and obtain several q-series identities by using the boson-boson correspondence.

Fingerprint Comparison and Adversarialism: The Scientific and Historical Evidence

AbstractThis article suggests that lawyers and courts are largely oblivious to scientific insights regarding the value and limitations of latent fingerprint evidence. It proceeds through a detailed historical analysis of the way fingerprint evidence has been reported and challenged. It compares legal responses with mainstream scientific research. Our analysis shows that fingerprint evidence is routinely equated with categorical proof of identity notwithstanding scientific warnings that such an approach is ‘indefensible’. We find that legal challenges to latent fingerprint evidence have been uniformly focused on adjectival issues (e.g. compliance with enabling legislation), leaving the validity and accuracy of this subjective comparison technique virtually unexamined since its first reception at the very beginning of the twentieth century. Lack of legal engagement with validity, error and scientific research suggest that adversarial procedures have not worked effectively to secure scientifically reliable expert evidence and that legal personnel struggle with elementary scientific reasoning.

On the Difference of Partial Theta Functions

Sums of the form $$\sum _{n\ge 0} (-1)^nq^{(n-1)n/2} x^n $$ are called partial theta functions. In his lost notebook, Ramanujan recorded many identities for those functions. In 2003, Warnaar found an elegant formula for a sum of two partial theta functions. Subsequently, Andrews and Warnaar established a similar result for the product of two partial theta functions. In this note, I discuss the relation between the Andrews–Warnaar identity and the (1986) product formula due to Gasper and Rahman. I employ nonterminating extension of Sears–Carlitz transformation for $$ _3\phi _2$$ to provide a new elegant proof for a companion identity for the difference of two partial theta series. This difference formula first appeared in the work of Schilling–Warnaar (Conjugate Bailey pairs from configuration sums and fractional-level string functions to Bailey’s lemma. Contemporary mathematics, American Mathematical Society, Providence, vol 297, pp 227–255, 2002). Finally, I show that Schilling–Warnnar (2002) and Warnaar (Proc Lond Math Soc 87:363–395, 2003) formulas are, in fact, equivalent.

Birth Certificates, Birth Registration and the Denial of Human Rights: Evidence from Tanzania National Panel Data 2010/11

In many countries, a birth certificate is necessary to attend school, receive health care, inherit property, open a bank account, gain access to credit, obtain other forms of identification, vote, and receive a death certificate (Hunter and Brill, 2016). A birth certificate is proof of identity, citizenship and serves as a gateway to the realisation of other rights for children. It also serves as evidence that a child has been registered. Using evidence from the Tanzania National Panel Data 2010/11, I show that birth registration predicts lower odds for possessing a birth certificate for children in Tanzania. Instead, the education of the mother and the ability of households to pay for their own malaria bed nets, serve as the strongest predictors for possessing birth certificates in Tanzania. The article concludes with recommendations for improving birth registration and certification in Tanzania.

General Colored Partition Identities

Ramanujan’s modular equations of degrees 3, 5, 7, 11 and 23 yield beautiful colored partition identities. Warnaar analytically generalized the modular equations of degrees 3 and 7, and thereafter, the author found bijective proofs of those partitions identities and recently, established an analytic generalization of the modular equations of degrees 5, 11 and 23. The partition identities of degrees 5 and 11 were combinatorially proved by Sandon and Zanello, and it remains open to find a combinatorial proof of the partition identity of degree 23. In this paper, we prove general colored partition identities with a restriction on the number of parts, which are connected to the partition identities arising from those modular equations. We also provide bijective proofs of these partition identities. In particular, one of these proofs gives bijective proofs of the partition identity of degree 23 for some cases, which also work for the identities of degrees 5 and 11 for the same cases.