A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states appearing for non-Hermitian Hamiltonians. We start with an investigation of the space of non-degenerate operators on a finite-dimensional state space. We then show how the energy bands of a Hamiltonian family form a covering space. Likewise, we show that the eigenrays form a bundle, a generalization of a principal bundle, which admits a natural connection yielding the (generalized) geometric phase. This bundle provides in addition a natural generalization of the quantum geometric tensor and derived tensors, and we show how it can incorporate the non-geometric dynamical phase as well. We finish by demonstrating how the bundle can be recast as a principal bundle, so that both the geometric phases and the permutations of eigenstates can be expressed simultaneously by means of standard holonomy theory.

Normal product form of two-mode Wigner operator

In the context of normal product, we use the method of the integration within an ordered product (IWOP) of operators to derive three representations of the two-mode Wigner operator: SU (2) symmetric description, SU (1, 1) symmetric description and polar coordinate form. We find that two-mode Wigner operator has multiple potential degrees of freedom. As the physical meaning of the selected integral variable changes, Wigner operator shows different symmetries. In particular, in the case of polar coordinates, we reveal the natural connection between the two-mode Wigner operator and the entangled state representation.

Follow the leader: Child-led inquiries to develop science learning of young children

Science education in the early years has been found to be lacking when compared to other content areas, specifically numeracy and literacy. It has been suggested that this lack of opportunity for young children to learn science is due to educator’s lack of confidence to teach science, fuelled by concerns regarding a reduced understanding of science concepts. For young children, however, science is everywhere and is embedded in all aspects of their lives as they explore and interact to make sense of the world around them. Given this natural connection to science, it is important for educators to notice and respond to children’s interest to encourage science learning to occur. This paper reports on an exploratory research study in which children took the leading role in inquiry-based interactions during off-site school days that took place within a metropolitan city zoo. Through the collection of observations and interactions with the research, several inquiries were documented. The children challenged the educators within the program to follow up on questions posed by them and engage the children across a broad age range in an inquiry to answer these questions.

Bath and the Body, Bamboo and the Soul

<p>Bathing at a fundamental level is desired for two attributes cleansing the body, and cleansing the soul. Historically the act of bathing has been a combination of hot and cold water bathing; this act cleanses both the body and soul, and is seen as an enjoyable pastime for both eastern and western cultures. The priority then is to architecturally express the 'body and soul' through a careful material selection. The choice of materials reflects this, concrete and bamboo, expressing the solid (body) and the light (soul). Design precedents, material comparison, eastern and western beliefs are used to establish a rationale between the material contrast of body and soul. The location for the design reflects the natural connection between 'body and soul' in a location that references the land and water, geothermal and steam, lake and landscape. The final project includes detailing of non-penetrating fixings for the use in bamboo construction, including natural and industrial products into a public bath that compliments the body and the soul.</p>

Bath and the Body, Bamboo and the Soul

<p>Bathing at a fundamental level is desired for two attributes cleansing the body, and cleansing the soul. Historically the act of bathing has been a combination of hot and cold water bathing; this act cleanses both the body and soul, and is seen as an enjoyable pastime for both eastern and western cultures. The priority then is to architecturally express the 'body and soul' through a careful material selection. The choice of materials reflects this, concrete and bamboo, expressing the solid (body) and the light (soul). Design precedents, material comparison, eastern and western beliefs are used to establish a rationale between the material contrast of body and soul. The location for the design reflects the natural connection between 'body and soul' in a location that references the land and water, geothermal and steam, lake and landscape. The final project includes detailing of non-penetrating fixings for the use in bamboo construction, including natural and industrial products into a public bath that compliments the body and the soul.</p>

A Nomadic Spirituality in the Dream of the Red Chamber: Seeking the Goddess in an Immanent Process

The multicultural work, The Dream of the Red Chamber, posits a field for exploring the interconnection between Confucian interpretations and its intrinsic Goddess narrative. In this article, I examine the reconciliation of the former with the latter. The immanent transcendence in Neo-Confucianism is not enough for interpreting this novel, for covering the question of a natural connection between Vermilion Pearl and Shen Ying, for a dichotomy of tian and the earth, the transcendent and the immanent. The Goddess narrative of repairing tian can rectify this difficult position and a nomadic spirituality forged in a mutually cultivating process is proposed, both to rescue the Confucian interpretation of the novel and to find a way of reconciling the Confucian ‘ tian’ and the Goddess.

ART - TELEVISION OR TELEVISION ART?

Автор рассматривает эстетическую природу телевидения, составляющие компоненты художественного образа, язык выразительных средств различных искусств и природную связь ТВ с кинематографом. The article examines the aesthetic nature of television, the components of the artistic image, the «language» of expressive means of arts and the natural connection of TV with cinema.

Fiscal Multipliers and Foreign Holdings of Public Debt

This paper explores a natural connection between fiscal multipliers and foreign holdings of public debt. Although fiscal expansions can raise domestic economic activity through various channels, they can also have crowding-out effects if the resources used to acquire public debt reduce domestic consumption and investment. These crowding-out effects are likely to be weaker when governments have access to foreign savings when selling their debt. We test this hypothesis for the US in the post-war period and for a panel of 17 advanced economies from the 1980s to the present. To do so, we assemble a novel database of public debt holdings by domestic and foreign creditors for these countries. We combine this data with standard measures of fiscal policy shocks and show that, indeed, the size of fiscal multipliers is increasing in the share of public debt held by foreigners. In particular, the fiscal multiplier is smaller than one when the foreign share is low, such as in the U.S. in the 1950s and 1960s and Japan today, and larger than one when the foreign share is high, such as in the U.S. and Ireland today.

School Police Reform: A Public Health Imperative

Out of the twin pandemics currently gripping the United States¬—deaths of unarmed Black victims at the hands of police and racialized health inequities resulting from COVID-19—an antiracist health equity agenda has emerged that identifies racism as a public health crisis. Likewise, calls for reform of school policing by those advocating for civil rights, racial justice, and Black Lives Matter have simultaneously intensified. Yet each remains siloed, despite the natural connection and implicit overlap between these separate movements and debates. Indeed, there are documented negative health effects of school policing for Black, Indigenous, people of color (BIPOC) youth. But these have gone largely ignored or underemphasized by the movement to reform school police. Similarly, the racial health equity movement has overlooked race-conscious health equity reforms to school policing. This Article aims to fill the gap by connecting these distinct movements and debates and articulating a public-health-based response to school policing.

A Generalization of the Bollobás Set Pairs Inequality

The Bollobás set pairs inequality is a fundamental result in extremal set theory with many applications. In this paper, for $n \geqslant k \geqslant t \geqslant 2$, we consider a collection of $k$ families $\mathcal{A}_i: 1 \leq i \leqslant k$ where $\mathcal{A}_i = \{ A_{i,j} \subset [n] : j \in [n] \}$ so that $A_{1, i_1} \cap \cdots \cap A_{k,i_k} \neq \varnothing$ if and only if there are at least $t$ distinct indices $i_1,i_2,\dots,i_k$. Via a natural connection to a hypergraph covering problem, we give bounds on the maximum size $\beta_{k,t}(n)$ of the families with ground set $[n]$.