Collapse Of Hierarchy Research Articles

Samhällen i förändring 300–700 e.Kr.

The aim of this article is to discuss the consequences of a decrease of population in the settled country south of today’s city of Malmö, A D 300–700. This development is interpreted as a dramatic reduction of settlements reflected in the number of farms and the sizes of long-houses. In A D 500–700 the settled area was of minimal extent. This was part of a general decrease of population, farms and settlements in Scandinavia during the Migration Period. The causes and effects of this decline are still under discussion. Itis however clear that the collapse of the social hierarchies and economies of the local communities south of Malmö had the consequence that the diminishing population did not take part in the regional social and political process towards an integrated and centralized social organization in southwest Scania.

Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation

Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement, and we present a class of bipartite states, called premeasurement states, for which several of these hierarchies collapse to a single value. Because premeasurement states are the kind of states produced when a system interacts with a measurement device, the hierarchy collapse implies that the uncertainty of an observable is quantitatively connected to the quantum correlations (entanglement, discord, etc.) produced when that observable is measured. This fascinating connection between uncertainty and quantum correlations leads to a reinterpretation of entropic formulations of the uncertainty principle, so-called entropic uncertainty relations, including ones that allow for quantum memory. These relations can be thought of as lower-bounds on the entanglement created when incompatible observables are measured. Hence, we find that entanglement creation exhibits complementarity, a concept that should encourage exploration into "entanglement complementarity relations".

Kernelization hardness of connectivity problems in [formula omitted]-degenerate graphs

A graph is d-degenerate if every subgraph contains a vertex of degree at most d. For instance, planar graphs are 5-degenerate. Inspired by the recent work by Philip, Raman and Sikdar, who have shown the existence of a polynomial kernel for Dominating Set in d-degenerate graphs, we investigate the kernelization complexity of problems that include a connectivity requirement in this class of graphs.Our main contribution is the proof that Connected Dominating Set does not admit a polynomial kernel in d-degenerate graphs for d≥2 unless NP⊆coNP/poly, which is known to cause a collapse of the polynomial hierarchy to its third level. We prove this using a problem that originates from bioinformatics–Colourful Graph Motif–analysed and proved to be NP-hard by Fellows et al. This problem nicely encapsulates the hardness of the connectivity requirement in kernelization. Our technique also yields an alternative proof that, under the same complexity assumption, Steiner Tree does not admit a polynomial kernel. The original proof, via a reduction from Set Cover, is due to Dom, Lokshtanov and Saurabh.We extend our analysis by showing that, unless NP⊆coNP/poly, there do not exist polynomial kernels for Steiner Tree, Connected Feedback Vertex Set and Connected Odd Cycle Transversal in d-degenerate graphs for d≥2. On the other hand, we show a polynomial kernel for Connected Vertex Cover in graphs that do not contain the biclique Ki,j as a subgraph. As a d-degenerate graph cannot contain Kd+1,d+1 as a subgraph, the results holds also for graphs of bounded degeneracy.

Superflat and the Postmodern Gothic: Images of Western Modernity in <i>Kuroshitsuji</i>

Superflat and the Postmodern Gothic: Images of Western Modernity in Kuroshitsuji Waiyee Loh (bio) In 2007, Toboso Yana began publishing Kuroshitsuji (Black Butler), a manga series set in late Victorian England about a beautiful butler named Sebastian, who is actually a devil in disguise, and his young master, Count Ciel Phantomhive. With its Western European setting, its aestheticization of the demonic and the deathly, and its penchant for roses, Rococo motifs, and the color black, Kuroshitsuji exemplifies a type of “Gothic” style that has become popular in postwar Japanese shōjo culture since Hagio Moto’s classic vampire manga Pō no ichizoku (1972–76, The clan of Poe).1 Through a reading of Kuroshitsuji as a representative case study, I examine this shōjo Gothic style and its relation to Japanese national identity in the age of postmodern globalization and post-colonial reevaluations of the legacy of nineteenth-century Western imperialism.2 In the first part of the essay, I consider the relationship between the superflat visual aesthetic and the postmodern condition of simulation, which the shōjo Gothic style makes explicit. I then discuss how the shōjo Gothic style, as a postmodern and postcolonial practice of enunciation, simulates, recontextualizes, and reinvents a Western European past in order to articulate the enduring desire of the contemporary Japanese nation for an idealized “Western modernity,” characterized by “tasteful” consumption. In the last [End Page 111] part of the essay, I argue that Kuroshitsuji, through its Gothic style, paradoxically intervenes in its own idealization of Western modernity to celebrate contemporary Japan’s ability to hybridize different cultures and to disseminate its hybrid cultural commodities around the world as a cultural superpower in the age of postmodern globalization. The shōjo Gothic style in Kuroshitsuji thus expresses the profound ambivalence of postcolonial Japanese national identity vis-à-vis the West in the twenty-first century. Through reinscribing the signs of a Western European past, Kuroshitsuji articulates the split in the Japanese “Self” between the endless striving for the ideal of “Western” modernity and the nationalistic affirmation of an empowered “Japanese” (post)modernity, while eliding the inherent cultural hybridity of the shōjo Gothic style and of the national identity articulated through this style. Lastly, it is important to note that Japan was (and is) a (neo)colonial power in Asia, and I touch on the significance of this double postcolonial relationship at the end of the essay. Murakami Takashi first introduced the concept of “superflat” within the context of an art exhibition titled Super Flat, which was presented in 2000 at the PARCO department store gallery. He later developed the concept through two more exhibitions: Coloriage (2002) and Little Boy: The Arts of Japan’s Exploding Subculture (2005). Murakami and several other critics, including Azuma Hiroki and Sawaragi Noi, interpret superflatness as a visual manifestation of the postmodern collapse of hierarchies and the fragmentation of the modern Cartesian subject.3 In this essay, I will argue that the shōjo Gothic style points to a connection between superflatness and another principal element of the postmodern condition: simulation. In “Postmodernism, or The Cultural Logic of Late Capitalism” (1984), Fredric Jameson reads the formal planarity of Andy Warhol’s Diamond Dust Shoes as a symbolic expression of “the emergence of a new kind of flatness or depthlessness, a new kind of superficiality” in our world where objects “now become a set of texts or simulacra.” 4 Likewise, the shōjo Gothic style suggests that the superflat visual aesthetic implies a particular postmodern mode of vision and knowledge—a “way of seeing” (John Berger) or “scopic regime” (Martin Jay)—that “flattens” all “real” phenomena in the world into hyperreal signifiers “without origin or reality.” 5 Kuroshitsuji illustrates this connection between literal and figurative flattening through its depiction of the Undertaker’s shop. In Figure 1, the façade of the shop is depicted in a highly planar, nongeometric perspectival [End Page 112] style. The figures of the characters, the door of the shop, and the coffin and tombstones flanking the door are positioned in a highly linear arrangement, and the speech bubbles add to the planarity through their superimposition, also in a linear fashion, over the picture...

Derek Walcott's The Odyssey: A Stage Version

Click to increase image sizeClick to decrease image size Notes 1. See Valérie Bada's ‘Derek Walcott's The Odyssey: A Post-Colonial “Odd Assay” of The Epic Genre as a Regenerative Source of “Latent Cross-Culturalities”’ in Crucible of Cultures: Anglophone Drama at the Dawn of a New Millenium, ed. Maruc Maufort and Franca Bellarsi (Brussels, Belgium: Peter Lang, 2002) for a discussion of the sea as metaphor for poetic site. 2. For a discussion of how meaning is created through the stichomythic half-lines of dialogue see Peter Burian's ‘You Can Build a Heavy-Beamed Poem Out of This’. The shared creation of meaning can be read as contributing to the collapse of hierarchies which the play promotes.

Counting classes and the fine structure between [formula omitted] and [formula omitted

The class N C 1 of problems solvable by bounded fan-in circuit families of logarithmic depth is known to be contained in logarithmic space L , but not much about the converse is known. In this paper we examine the structure of classes in between N C 1 and L based on counting functions or, equivalently, based on arithmetic circuits. The classes P NC 1 and C = NC 1 , defined by a test for positivity and a test for zero, respectively, of arithmetic circuit families of logarithmic depth, sit in this complexity interval. We study the landscape of Boolean hierarchies, constant-depth oracle hierarchies, and logarithmic-depth oracle hierarchies over P NC 1 and C = NC 1 . We provide complete problems, obtain the upper bound L for all these hierarchies, and prove partial hierarchy collapses. In particular, the constant-depth oracle hierarchy over P NC 1 collapses to its first level P NC 1 , and the constant-depth oracle hierarchy over C = NC 1 collapses to its second level.

Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy

We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically, we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, either exactly in total variation distance or even approximately up to 41 per cent multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on onlylines then it may, in fact, be classically efficiently sampled.

Approximate counting by hashing in bounded arithmetic

AbstractWe show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the collapse of the polynomial-time hierarchy.

Raising an Empire: Children in Early Modern Iberia and Colonial Latin America

Youth is coming of age in Latin American history, or so it seems with recent studies on children and childhood. González and Premo’s edited volume contributes to the field by studying children as an extension of empire in the early modern Iberian world. The editors set out to present various alternatives for the study of childhood in the Iberian world. The first alternative is to unhitch the history of childhood from the history of modernity, a connection proposed by Philippe Ariès in his pioneering work on European childhood. Rather than assuming children to be hidden and silent, researchers can find them in often-used sources such as criminal, notary, and institutional records and court cases. By reading such sources for children, they emerge not only as objects of historical research but as “key colonial subjects” (p. 243).Two chapters, by Isabel dos Guimãres Sá and Valentina Tikoff, look at children in the Iberian Peninsula. While Sá’s chapter is largely an overview of children in Portugal, in particular children in the royal court, Tikoff examines elite and common children placed in Seville’s various institutions for children and the strategic use of institutions, even orphanages, by parents as a means to educate and feed children. A flexible interpretation of the category of “orphan” made it possible for parents to secure social mobility through state beneficence and discipline.The theme of strategies for survival is raised again in the chapter on indigenous migration to Lima in the early colonial period. Using principally the 1613 census of Lima, Teresa Vergara asks us to assume that indigenous parents migrated to the city for a better life for their children, and that they subsequently placed their children in the homes of other people whom they “trusted would treat [their children] well.” While this might have been “a strategy that allowed them [indigenous families] to cope with the colonial system,” this explanation might risk downplaying the very coercive actions of the colonial state for labor extraction that pushed some families to take such extreme measures.The argument that the labor needs of adults determined the lives of some children is made by Laura Shelton, who describes the “adoption” of children to fill the labor shortages suffered by Sonoran ranchers and agriculturalists. This ad hoc labor scheme took advantage of an informal social practice of passing along children to family members and non-kin. According to Shelton, when it came down to who held the rights of patria potestad in custody battles, the colonial courts tended to side in favor of patron-guardians. Yet, the fact that parents who could afford to repay childcare expenses could thus recover their children suggests another possible interpretation, that parents maintained their rights (if they had the money).The connection between the maintenance of empire and the fate of children comes to the foreground in the chapters by Ondina González and Ann Twinam. González studies the establishment of a foundling home in Havana, the apparent need for such an institution, and its doomed fate as a consequence of lack of financial support from the local elite. Twinam’s chapter moves to the late eighteenth century and gives a nuanced study of the racial and gender considerations of abandoned babes (expósitos) and Bourbon legislation that wished to erase the stain of illegitimacy suffered by those of unknown parentage. The potential collapse of racial hierarchy due to such blanket legislation led to an ultimately successful battle by local elites to protect “white” privilege.The fragility and insecurity of children’s lives is most heart-wrenchingly described in Elizabeth Kuznesof’s thoughtful chapter on slave children in Brazil. This chapter successfully combines a historiographical overview with new readings of established research into children. While the fortune of poor Brazilian children was bleak in general, children born into slavery were “vulnerable to being separated from family members at any point” (p. 189).It is perhaps in terms of the editors’ goal of hearing children’s voices (or at least their “echoes”) that this collection of essays falls short. In the chapter “Ursula: The Life and Times of an Aristocratic Girl in Santiago, Chile (1666 – 1678),” Jorge Rojas Flores comes the closest to directly citing a child, though not in a child’s voice but that of an adult woman reflecting on her childhood for the purposes of a religious autobiography. For the most part, children remain on the margins of adults’ lives as contested property (in custody battles over child servants), as normalized citizens formed in institutions, or as the subjects of legal and religious prescriptions. However, as this volume shows, we can learn much about social practices, normative views of childhood, labor systems, and indeed the building and maintaining of empire through the study of the smallest of subjects, a colonial child.

Does the Polynomial Hierarchy Collapse if Onto Functions are Invertible?

The class TFNP, defined by Megiddo and Papadimitriou, consists of multivalued functions with values that are polynomially verifiable and guaranteed to exist. Do we have evidence that such functions are hard, for example, if TFNP is computable in polynomial-time does this imply the polynomial-time hierarchy collapses? By computing a multivalued function in deterministic polynomial-time we mean on every input producing one of the possible values of the function on that input.We give a relativized negative answer to this question by exhibiting an oracle under which TFNP functions are easy to compute but the polynomial-time hierarchy is infinite. We also show that relative to this same oracle, P≠UP and TFNPNP functions are not computable in polynomial-time with an NP oracle.

On the Hierarchy of Intuitionistic Bounded Arithmetic

In this article, we study the two hierarchies of intuitionistic bounded arithmetic introduced by Buss and Harnik. Harnik's hierarchy contains the theory IS21 defined and studied by Cook and Urquhart as the first level. We prove level by level equivalence between the two hierarchies (for the first level, the fact was first proved by Cook and Urquhart using realizability and functional interpretation and later by Buss by an elementary method). Next we investigate the question of whether the hierarchy, denoted IS2i⁠, collapses. We show that if IS2i⊢IS2i+1⁠, then S2i(PV)⊢Σib=Πib and so the polynomial hierarchy collapses to Σip=Πip⁠. Our proof for this is independent from earlier works on relating the collapse of the hierarchy of classical bounded arithmetic and the collapse of the polynomial hierarchy. We give an elementary model theoretic proof using only the basic properties of the theories IS2i and we do not use results which belong to Cook and Urquhart and also Harnik that characterize the definable functions of these theories with long witnessing proofs.

On the Power of Unambiguity in Alternating Machines

Unambiguity in alternating Turing machines has received considerable attention in the context of analyzing globally unique games by Aida et al. [ACRW] and in the design of efficient protocols involving globally unique games by Crasmaru et al. [CGRS]. This paper explores the power of unambiguity in alternating Turing machines in the following settings: 1. We show that unambiguity-based hierarchies-AUPH, UPH, and UPH-are infinite in some relativized world. For each $k \geq 2$, we construct another relativized world where the unambiguity-based hierarchies collapse so that they have exactly k distinct levels and their k-th levels coincide with PSPACE. These results shed light on the relativized power of the unambiguity-based hierarchies, and parallel the results known for the case of the polynomial hierarchy. 2. For every $k \ge 1$, we define the bounded-level unambiguous alternating solution class UAS(k) as the class of all sets L for which there exists a polynomial-time alternating Turing machine N, which need not be unambiguous on every input, with at most k alternations such that $x\in L$ if and only if x is accepted unambiguously by N. We construct a relativized world where, for all $k \geq 1, {\rm UP}_{\leq k} \subset {\rm UP}_{\leq k+1}$ and ${\rm UAS}(k) \subset {\rm UAS}(k+1)$. 3. Finally, we show that robustly k-level unambiguous alternating polynomial-time Turing machines, i.e., polynomial-time alternating Turing machines that for every oracle have k alternating levels and are unambiguous, accept languages that are computable in ${\rm P}^{\Sigma^{p}_{k} \oplus {\cal A}}$, for every oracle A. This generalizes a result of Hartmanis and Hemachandra [HH].

Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy

If every language in coNP has a constant-round interactive proof system, then the polynomial-time hierarchy collapses [R.B. Boppana, J. Håstad, S. Zachos, Does co-NP have short interactive proofs? Information Processing Letters 25 (2) (1987) 127–132]. On the other hand, the well-known LFKN protocol gives O ( n ) -round interactive proof systems for all languages in coNP [C. Lund, L. Fortnow, H. Karloff, N. Nisan, Algebraic methods for interactive proof systems, Journal of the Association for Computing Machinery 39 (4) (1992) 859–868]. We consider the question of whether it is possible for coNP to have interactive proof systems with polylogarithmic-round complexity. We show that this is unlikely by proving that if a coNP-complete set has a polylogarithmic-round interactive proof system, then the exponential-time hierarchy collapses. We also consider exponential versions of the Karp–Lipton theorem and Yap’s theorem.

The power of AIDS: kinship, mobility and the valuing of social and ritual relationships in Tanzania

The HIV/AIDS epidemic in Africa has become a test case of the effects of globalisation, in that it demonstrates how international processes may affect regional life situations and how 'the local' can simultaneously develop in its own way, through the processes of appropriating, modifying, and resisting global influences. Drawing on fieldwork in Tanzania, I show how the Luo in the Mara region define HIV/AIDS as an outcome of modernity and globalisation, which to them have become embodied in processes of migration, the collapse of generational and gender hierarchies, and an increased immorality in contemporary society. While social and moral ruptures in Mara become further condensed in tensions between lineages and AIDS-sick relatives, mourning and burial rituals (including widow cleansing), disputes over inheritance rights, and the attribution of illness to the breaking of a taboo (chira) have become essential for negotiating and maintaining social and cultural relationships in an era of AIDS. In conclusion I argue that the concepts of vitality and moral practice may assist an understanding of how different social actors in sub-Saharan Africa have responded to the breakdowns associated with increased suffering and death, and to describe some social and moral developments observable in the context of internationally driven public health campaigns in the region.

Nondeterministic ordered binary decision diagrams with repeated tests and various modes of acceptance

Ordered binary decision diagrams with repeated tests are considered both in complexity theory and in applications. Bollig et al. have proved in [B. Bollig, M. Sauerhoff, D. Sieling, I. Wegener, Hierarchy theorems of kOBDDs and kIBDDs, Theoret. Comput. Sci. 205 (1998) 45–60] a tight hierarchy result for the classes of functions representable by k layers of polynomial-size deterministic ordered binary decision diagrams. In this paper the nondeterministic case is investigated, where the layers are driven by one and the same variable ordering. For k being a constant, it is shown that for the existential, the parity-, and the majority acceptance mode the analogous hierarchy collapses.

Guest column: inapproximability results via Long Code based PCPs

Summer has come again. And what better way is there to spend a summer than to relax on a sandy beach, on a mountain top, or at a park's picnic tables, and... think theory ! Summer is a particularly good time to attack the big questions whose openness just plain annoys you. In light of Reingold's L = SL result, does L-vs.-RL tempt you? If so, take it on! (But perhaps peek first at Reingold--Trevisan--Vadhan's ECCC TR05-022.) Are you convinced that UP = NP should imply the collapse of the polynomial hierarchy? Make it so! (But if you hope to do so via showing that UP is contained in the low hierarchy, peek first at Long--Sheu's 1996 MST article.) You know that S 2 ⊆ S NP∩coNP 2 ⊆ ZPP NP and S NP 2 ⊆ ZPP NP NP , but believe that some of those "⊆"s are "=" s or are (gasp!) provably strict containments (thus giving some insight into whether recent improvements (Cai in FOCS 2001; Cai et al. in Information and Computation 2005) in the collapses of the polynomial hierarchy from assumptions that NP is in P/poly, (NP ∩ coNP)/poly, or coNP/poly are strict improvements)? Well, prove an "=" or find evidence for a strict containment... or to really make this a summer for us all to remember, prove a strict containment! Wishing you happy theorems.This article gives an overview of recent PCP constructions based on the Long Code and the inapproximability results implied by these constructions. We cover the inapproximability results for (1) MAX-3SAT and CLIQUE (2) Results for SPARSEST CUT, VERTEX COVER and MAX-CUT implied by the Unique Games Conjecture and (3) HYPERGRAPH VERTEX COVER and coloring problems on hypergraphs. The article aims at explaining the general framework that, loosely speaking, incorporates all the above results.

Extending Downward Collapse from 1-versus-2 Queries tom-versus-m+ 1 Queries

The top part of Figure 1.1 shows some classes from the (truth-table) bounded-query and boolean hierarchies. It is well known that if either of these hierarchies collapses at a given level, then all higher levels of that hierarchy collapse to that same level. This is a standard upward translation of that has been known over a decade. The issue of whether these hierarchies can translate equality downwards has proven vastly more challenging. In particular, with regard to Figure 1.1, consider the following claim: \[ \psigkmtt = \psigkmponett \implies \diffmsigk = \codiffmsigk = \bh(\sigmak). (*) \] This claim, if true, says that equality translates downwards between levels of the bounded-query hierarchy and the boolean hierarchy levels that (before the fact) are immediately below them. Until recently, it was not known whether (*) ever held, except the degenerate cases = 0 and k = 0. Then Hemaspaandra, Hemaspaandra, and Hempel [SIAM J. Comput., 28 (1999), pp. 383--393] proved that (*) holds all m, k > 2. Buhrman and Fortnow [J. Comput. System Sci., 59 (1999), pp. 182--199] then showed that, when k = 2, (*) holds the case = 1. In this paper, we prove that the case k = 2, (*) holds all values of m. Since there is an oracle relative to which for k = 1, (*) holds all m fails (see Buhrman and Fortnow), our achievement of the k = 2 case cannot be strengthened to k = 1 by any relativizable proof technique. The new downward translation we obtain also tightens the collapse in the polynomial hierarchy implied by a collapse in the bounded-query hierarchy of the second level of the polynomial hierarchy.

Racism: A Short History

Back to table of contents Previous article Next article Book ReviewsFull AccessRacism: A Short HistoryJoshua Miller, Ph.D.Joshua MillerSearch for more papers by this author, Ph.D.Published Online:1 Apr 2004https://doi.org/10.1176/appi.ps.55.4.459-aAboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail George M. Fredrickson is a major figure among historians of race and racism. In this book he has written a short history of Western racism that is concise, intelligent, informative, and well written. In three chapters he traces the early seeds of racism, its rise during the modern era, and its "hideous fruition" and eventual rejection in the 20th century. He also includes an epilogue that ponders the contours of racism in the 21st century and an appendix that traces racism as a concept in historical discourse.As a historian, Fredrickson paints his portrait of racism with bold strokes. He defines racism in his final sentence as occurring when "one ethnic group or historical collectivity dominates, excludes, or seeks to eliminate another on the basis of differences that it believes are hereditary and unalterable." Although viewing religious intolerance as a close cousin of racism, Fredrickson distinguishes it by virtue of its focus on beliefs rather than an essentialist notion of human difference.Fredrickson considers the irony of how the ascendancy of science and reasoning in Europe in the 18th and 19th centuries and the collapse of theological and monarchical hierarchies both justified racism through a kind of "racial Darwinism," while also offering the vision and ethics to challenge racism through appeals to liberty and egalitarianism. The philosopher Charles Mills meditates on this idea in-depth in his excellent book, The Racial Contract (1).The three case studies of modern racism that Frederickson concentrates on are the Holocaust, apartheid in South Africa, and institutionalized racism in the southern United States. Fredrickson is more cautious about applying the term "racism" than are many social scientists and psychologists. He is concerned with the most extreme and systematic forms of racism and does not consider racism's more subtle manifestations, such as "aversive racism" (2) or "racial microagressions" (3). It would have been interesting to read more about his impressions of the United States today and how Fredrickson would characterize the burgeoning prison population that has such disproportionately high numbers of African-American and Latino inmates, or the enduring patterns of residential and school segregation.Racism: A Short History does not articulate the dynamics of racism in psychiatry today but does offer a useful, succinct description of racism's history in the Western world, which provides an important foundation for practitioners grappling to understand the impact of racism on our clients, on our work, and on ourselves.Dr. Miller is a professor at Smith College School of Social Work and chair of the school's social policy sequence.by George M. Fredrickson; Princeton, New Jersey, Princeton University Press, 2002, 216 pages, $22.95 softcover

Tree-width and the monadic quantifier hierarchy

It is well known that on classes of graphs of bounded tree-width, every monadic second-order property is decidable in polynomial time. The converse is not true without further assumptions. It follows from the work of Robertson and Seymour, that if a class of graphs K has unbounded tree-width and is closed under minors, then K contains all planar graphs. But on planar graphs, three-colorability is NP-complete. Hence, if P≠NP and on K every existential monadic second-order property is in P, then K has bounded tree-width. In other words, for K closed under minors, K is of bounded tree-width iff all monadic second-order properties are decidable in~ P . In this note we prove that in order to characterize classes of graphs of bounded tree-width where the monadic quantifier hierarchy collapses, closure under minors can be replaced by closure under topological minors. Closure under minors of K implies that K is in P, whereas we also note that there is a class of graphs K closed under topological minors which is not even r.e. We also show, that closure under induced subgraphs or even under subgraphs alone does not suffice to show that the collapse of the monadic quantifier hierarchy on K implies that K is of bounded tree-width or clique-width. Other characterizations of classes of bounded tree-width in terms of collapses of the monadic quantifier hierarchy to levels above the existential are discussed.

Strengths and Weaknesses of LH Arithmetic

In this paper we provide a new arithmetic characterization of the levels of the og-time hierarchy (LH). We define arithmetic classes and that correspond to -LOGTIME and -LOGTIME, respectively. We break and into natural hierarchies of subclasses and . We then define bounded arithmetic deduction systems ′ whose -definable functions are precisely B(-LOGTIME). We show these theories are quite strong in that (1) LIOpen proves for any fixed m that , (2) TAC, a theory that is slightly stronger than ′ whose (LH)-definable functions are LH, proves LH is not equal to -TIME(s) for any m> 0, where 2s ∈L, s(n) ∈ ω(log n), and (3) TAC proves LH ≠ for all k and m. We then show that the theory TAC cannot prove the collapse of the polynomial hierarchy. Thus any such proof, if it exists, must be argued in a stronger systems than ours.