We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from a unified perspective. For groups acting on trees, we introduce a dynamical condition that allows us to deduce the power alternative for the group from the power alternative for its stabilisers of points. As an application, we reduce the power alternative for Artin groups to the power alternative for free-of-infinity Artin groups, under some conditions on their parabolic subgroups. We also introduce a uniform version of the power alternative and prove it, among other things, for a large family of two-dimensional Artin groups. As a corollary, we deduce that these Artin groups have uniform exponential growth. Finally, we prove that the power alternative is stable under taking relatively hyperbolic groups. We apply this to show that various examples, including all free-by-$\mathbb{Z}$ groups and a natural subclass of hierarchically hyperbolic groups, satisfy the uniform power alternative.
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh perspective on their structural properties. We showed that partially alternative algebras exist in any even dimension. Then we classified middle $\mathbb C$-associative (noncommutative) algebras satisfying partial alternativity condition. We demonstrated that for any four-dimensional partially alternative real division algebra, one can select a basis that significantly simplifies its multiplication table. Furthermore, we established that every four-dimensional partially alternative real division algebra naturally gives rise to a real Lie algebra, thereby bridging these two important algebraic frameworks. Our work culminates in a description of all Lie algebras arising from such partially alternative algebras. These results extend our understanding of algebraic structures and reveal new connections between different types of algebras.
The algebraic and geometric classifications of complex $3$-dimensional right alternative and semi-alternative algebras are given. As corollaries, we have the algebraic and geometric classification of complex $3$-dimensional $\mathfrak{perm}$, binary $\mathfrak{perm}$, associative, $(-1,1)$-, binary $(-1,1)$-, and assosymmetric algebras. In particular, we proved that the first example of non-associative right alternative algebras appears in dimension $3;$ the first example of non-associative assosymmetric algebras appears in dimension $3;$ the first example of non-assosymmetric semi-alternative algebras appears in dimension $4;$ the first example of binary $(-1,1)$-algebras, which is non-$(-1,1)$-, appears in dimension $4;$ the first example of right alternative algebras, which is not binary $(-1,1)$-, appears in dimension $4;$ the first example of binary $\mathfrak{perm}$ non-$\mathfrak{perm}$ algebras appears in dimension $4.$ As a byproduct, we give a more easy answer to problem 2.109 from the Dniester Notebook, previously resolved by Shestakov and Arenas.
We introduce the ratio of the number of roots of a polynomial $P_{d}$, less than one in modulus, to its degree $d$ as an alternative to Mahler measure. We investigate some properties of the alternative. We generalise this definition for a polynomial in several variables using Cauchy's argument principle. If a polynomial in two variables do not vanish on the torus we prove the theorem for the alternative which is analogous to the Boyd-Lawton limit formula for Mahler measure. We determined the exact value of the alternative of $1+x+y$ and $1+x+y+z$. Numerical calculations suggest a conjecture about the exact value of the alternative of such polynomials having more than three variables.
In this paper, a nilpotency criterion is given for finite dimensional alternative superalgebras in the spirit of Engel's Theorem for Jordan superalgebras over infinite fields provided by Shestakov and Okunev. For alternative superalgebras, no restrictions on the cardinality of the ground field are required. Furthermore, we establish some connections between the concepts of graded-nil and nilpotent alternative superalgebras, and we also exhibit an example of an Engelian commutative power-associative superalgebra of dimension $4$ which is not nilpotent.
Since the original derivation of Hawking radiation, there have been lots of alternative approaches to show the same fact that black holes emit particles as hot bodies with a temperature. These alternative methods generally rely on different conditions and physical quantities to manifest the radiation, providing various points of view of this effect in the intersection of gravity and quantum theory. This chapter presents some alternative derivations of Hawking radiation in the literature, including the tunneling, anomaly and Green's function methods. From these methods, various features of the black hole system can be seen, such as the gravitational and trace anomalies of the $(1+1)$-dimensional effective theory and the analytical continuation of the complexified spacetime.
Alternative routing is crucial to minimize the environmental impact of urban transportation while enhancing road network efficiency and reducing traffic congestion. Existing methods neglect information about road popularity, possibly leading to unintended consequences such as increasing emissions and congestion. This paper introduces Polaris, an alternative routing algorithm that exploits road popularity to optimize traffic distribution and reduce CO2 emissions. Polaris leverages the novel concept of K-road layers, which mitigates the feedback loop effect where redirecting vehicles to less popular roads could increase their popularity in the future. We conduct experiments in three cities to evaluate Polaris against state-of-the-art alternative routing algorithms. Our results demonstrate that Polaris significantly reduces the overuse of highly popular road edges and traversed regulated intersections, showcasing its ability to generate efficient routes and distribute traffic more evenly. Furthermore, Polaris achieves substantial CO2 reductions, outperforming existing alternative routing strategies. Finally, we compare Polaris to an algorithm that coordinates vehicles centrally to dis
We introduce a notion of pre-alternative algebra which may be seen as an alternative algebra whose product can be decomposed into two pieces which are compatible in a certain way. It is also the "alternative" analogue of a dendriform dialgebra or a pre-Lie algebra. The left and right multiplication operators of a pre-alternative algebra give a bimodule structure of the associated alternative algebra. There exists a (coboundary) bialgebra theory for pre-alternative algebras, namely, pre-alternative bialgebras, which exhibits all the familiar properties of the famous Lie bialgebra theory. In particular, a pre-alternative bialgebra is equivalent to a phase space of an alternative algebra and our study leads to what we called $PA$-equations in a pre-alternative algebra, which are analogues of the classical Yang-Baxter equation.
Bell's states are among the most useful in quantum computing. These state are an orthonormal base of entagled states with two qubits. We propose alternative bases of entangled states. Some of these states depend on a continuous parameter. We present the quantum circuit and code of these alternative bases. In addition, we study quantum teleportation with these entangled states and present their quantum circuits and codes associated.
In this submission, I discuss my research on values, norms and practices of subcultures formed as an "alternative" to the dominant way of life. In particular, I explore how the Internet of Things (IoT) or intelligent agents relates to alternative forms of interaction or be understood and reconstructed through alternative concepts or frameworks. For the past three years I have been conducting fieldwork on communities pursuing alternative lifestyles. This work considers how those alternative lifestyles may contribute to an understanding of objects, spaces in future smart home. Through my fieldwork and research through design, I hope to offer an alternative vision to living with IoT and envision future domesticity in a unique and even groundbreaking way.
CONTEXT: A prior national survey documented the high prevalence and costs of alternative medicine use in the United States in 1990. OBJECTIVE: To document trends in alternative medicine use in the United States between 1990 and 1997. DESIGN: Nationally representative random household telephone surveys using comparable key questions were conducted in 1991 and 1997 measuring utilization in 1990 and 1997, respectively. PARTICIPANTS: A total of 1539 adults in 1991 and 2055 in 1997. MAIN OUTCOMES MEASURES: Prevalence, estimated costs, and disclosure of alternative therapies to physicians. RESULTS: Use of at least 1 of 16 alternative therapies during the previous year increased from 33.8% in 1990 to 42.1% in 1997 (P < or = .001). The therapies increasing the most included herbal medicine, massage, megavitamins, self-help groups, folk remedies, energy healing, and homeopathy. The probability of users visiting an alternative medicine practitioner increased from 36.3% to 46.3% (P = .002). In both surveys alternative therapies were used most frequently for chronic conditions, including back problems, anxiety, depression, and headaches. There was no significant change in disclosure rates between the 2 survey years; 39.8% of alternative therapies were disclosed to physicians in 1990 vs 38.5% in 1997. The percentage of users paying entirely out-of-pocket for services provided by alternative medicine practitioners did not change significantly between 1990 (64.0%) and 1997 (58.3%) (P=.36). Extrapolations to the US population suggest a 47.3% increase in total visits to alternative medicine practitioners, from 427 million in 1990 to 629 million in 1997, thereby exceeding total visits to all US primary care physicians. An estimated 15 million adults in 1997 took prescription medications concurrently with herbal remedies and/or high-dose vitamins (18.4% of all prescription users). Estimated expenditures for alternative medicine professional services increased 45.2% between 1990 and 1997 and were conservatively estimated at $21.2 billion in 1997, with at least $12.2 billion paid out-of-pocket. This exceeds the 1997 out-of-pocket expenditures for all US hospitalizations. Total 1997 out-of-pocket expenditures relating to alternative therapies were conservatively estimated at $27.0 billion, which is comparable with the projected 1997 out-of-pocket expenditures for all US physician services. CONCLUSIONS: Alternative medicine use and expenditures increased substantially between 1990 and 1997, attributable primarily to an increase in the proportion of the population seeking alternative therapies, rather than increased visits per patient.
Let A and A' be two alternative *-algebras with identities 1_A and 1_A', respectively, and e_1 and e_2 = 1_A - e_1 nontrivial symmetric idempotents in A. In this paper we study the characterization of multiplicative *-Jordan-type maps on alternative algebras.
CONTEXT: Research both in the United States and abroad suggests that significant numbers of people are involved with various forms of alternative medicine. However, the reasons for such use are, at present, poorly understood. OBJECTIVE: To investigate possible predictors of alternative health care use. METHODS: Three primary hypotheses were tested. People seek out these alternatives because (1) they are dissatisfied in some way with conventional treatment; (2) they see alternative treatments as offering more personal autonomy and control over health care decisions; and (3) the alternatives are seen as more compatible with the patients' values, worldview, or beliefs regarding the nature and meaning of health and illness. Additional predictor variables explored included demographics and health status. DESIGN: A written survey examining use of alternative health care, health status, values, and attitudes toward conventional medicine. Multiple logistic regression analyses were used in an effort to identify predictors of alternative health care use. SETTING AND PARTICIPANTS: A total of 1035 individuals randomly selected from a panel who had agreed to participate in mail surveys and who live throughout the United States. MAIN OUTCOME MEASURE: Use of alternative medicine within the previous year. RESULTS: The response rate was 69%. The following variables emerged as predictors of alternative health care use: more education (odds ratio [OR], 1.2; 95% confidence interval [CI], 1.1-1.3); poorer health status (OR, 1.3; 95% CI, 1.1-1.5); a holistic orientation to health (OR, 1.4; 95% CI, 1.1-1.9); having had a transformational experience that changed the person's worldview (OR, 1 .8; 95% CI, 1 .3-2.5); any of the following health problems: anxiety (OR, 3.1; 95% CI, 1.6-6.0); back problems (OR, 2.3; 95% CI, 1 .7-3.2); chronic pain (OR, 2.0; 95% CI, 1.1 -3.5); urinarytract problems (OR, 2.2; 95% CI, 1.3-3.5); and classification in a cultural group identifiable by their commitment to environmentalism, commitment to feminism, and interest in spirituality and personal growth psychology (OR, 2.0; 95% CI, 1.4-2.7). Dissatisfaction with conventional medicine did not predict use of alternative medicine. Only 4.4% of those surveyed reported relying primarily on alternative therapies. CONCLUSION: Along with being more educated and reporting poorer health status, the majority of alternative medicine users appear to be doing so not so much as a result of being dissatisfied with conventional medicine but largely because they find these health care alternatives to be more congruent with their own values, beliefs, and philosophical orientations toward health and life.
We introduce the concept of braided alternative bialgebra. The theory of cocycle bicrossproducts for alternative bialgebras is developed. As an application, the extending problem for alternative bialgebra is solved by using some non-abelian cohomology theory.
We develop a model of electoral accountability with mainstream and alternative media. In addition to regular high- and low-competence types, the incumbent may be an aspiring autocrat who controls the mainstream media and will subvert democracy if retained in office. A truthful alternative media can help voters identify and remove these subversive types while re-electing competent leaders. A malicious alternative media, in contrast, spreads false accusations about the incumbent and demotivates policy effort. If the alternative media is very likely be malicious and hence is unreliable, voters ignore it and use only the mainstream media to hold regular incumbents accountable, leaving aspiring autocrats to win re-election via propaganda that portrays them as effective policymakers. When the alternative media's reliability is intermediate, voters heed its warnings about subversive incumbents, but the prospect of being falsely accused demotivates effort by regular incumbents and electoral accountability breaks down.
The only systematic mapping of the HLAI technical landscape was conducted at a workshop in 2009 [Adams et al., 2012]. However, the results from it were not what organizers had hoped for [Goertzel 2014, 2016], merely just a series of milestones, up to 50% of which could be argued to have been completed already. We consider two more recent articles outlining paths to human-like intelligence [Mikolov et al., 2016; Lake et al., 2017]. These offer technical and more refined assessments of the requirements for HLAI rather than just milestones. While useful, they also have limitations. To address these limitations we propose the use of alternative techniques for an updated systematic mapping of the paths to HLAI. The newly proposed alternative techniques can model complex paths of future technologies using intricate directed graphs. Specifically, there are two classes of alternative techniques that we consider: scenario mapping methods and techniques for eliciting expert opinion through digital platforms and crowdsourcing. We assess the viability and utility of both the previous and alternative techniques, finding that the proposed alternative techniques could be very beneficial in advanc
Alphanumeric authentication routinely fails to regulate access to resources with the required stringency, primarily due to usability issues. Initial deployment did not reveal the problems of passwords, deep and profound flaws only emerged once passwords were deployed in the wild. The need for a replacement is widely acknowledged yet despite over a decade of research into knowledge-based alternatives, few, if any, have been adopted by industry. Alternatives are unconvincing for three primary reasons. The first is that alternatives are rarely investigated beyond the initial proposal, with only the results from a constrained lab test provided to convince adopters of their viability. The second is that alternatives are seldom tested realistically where the authenticator mediates access to something of value. The third is that the testing rarely varies the device or context beyond that initially targeted. In the modern world different devices are used across a variety of contexts. What works well in one context may easily fail in another. Consequently, the contribution of this paper is an "in the wild" evaluation of an alternative authentication mechanism that had demonstrated promise i
The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between nontrivial zeros is supposed to always lie at a half integer. It is known that the Alternative Hypothesis is compatible with what is known about the pair correlation function of zeta zeros. We ask whether what is currently known about higher correlation functions of the zeros is sufficient to rule out the Alternative Hypothesis and show by construction of an explicit counterexample point process that it is not. A similar result was recently independently obtained by T. Tao, using slightly different methods. We also apply the ergodic theorem to this point process to show there exists a deterministic collection of points lying in $\tfrac{1}{2}\mathbb{Z}$ which satisfy the Alternative Hypothesis spacing but mimic all statistics which are currently known about zeros of the zeta function.
It is shown that every multiplicative right Hom-alternative algebra is both Hom-power associative and Hom-Jordan admissible. Multiplicative right Hom-alternative algebras admit Albert-type decompositions with respect to idempotents. Multiplication operators defined by idempotents in right Hom-alternative algebras are studied. Hom-versions of some well-known identities in right alternative algebras are proved.
We prove the Girth Alternative for a sub-class of the HNN extensions of finitely generated groups. We also produce counterexamples to show that beyond our class, the alternative fails in general.