Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Death in the Bolivian High Plateau : Burials and Tiwanaku Society

My Ph.D. dissertation presents a multi-disciplinary analysis of the mortuary practices of the Tiwanaku culture of the Bolivian high plateau, situated at an altitude of c. 3800 m above sea level. The Tiwanaku State (c. AD 500-1150) was one of the most important pre-Inca civilisations of the South Central Andes. The book begins with a brief introductory chapter. In chapter 2 I discuss methodological and theoretical developments in archaeological mortuary studies from the late 1960s until the turn of the millennium. I am especially interested in the issue how archaeological burial data can be used to draw inferences on the social structure of prehistoric societies. Chapter 3 deals with the early historic sources written in the 16th and 17th centuries, following the Spanish Conquest of the Incas. In particular, I review information on how the Incas manifested status differences between and within social classes and what kinds of burial treatments they applied. In chapter 4 I compare the Inca case with 20th century ethnographic data on the Aymara Indians of the Bolivian high plateau. Even if Christianity has affected virtually every level of Aymara religion, surprisingly many traditional features can still be observed in present day Aymara mortuary ceremonies. The archaeological part of my book begins with chapter 5, which is an introduction into Tiwanaku archaeology. In the next chapter, I present an overview of previously reported Tiwanaku cemeteries and burials. Chapter 7 deals with my own excavations at the Late Tiwanaku/early post-Tiwanaku cemetery site of Tiraska, located on the south-eastern shore of Lake Titicaca. During the 1998, 2002, and 2003 field seasons, a total of 32 burials were investigated at Tiraska. The great majority of these were subterranean stone-lined tombs, each containing the skeletal remains of 1 individual and 1-2 ceramic vessels. Nine burials have been radiocarbon dated, the dates in question indicating that the cemetery was in use from the 10th until the 13th century AD. In chapter 8 I point out that considerable regional and/or ethnic differences can be noted between studied Tiwanaku cemetery sites. Because of the mentioned differences, and a general lack of securely dated burial contexts, I feel that at present we can do no better than to classify most studied Tiwanaku burials into three broad categories: (1) elite and/or priests, (2) "commoners", and (3) sacrificial victims and/or slaves and/or prisoners of war. On the basis of such indicators as monumental architecture and occupational specialisation we would expect to find considerable status-related differences in tomb size, grave goods, etc. among the Tiwanaku. Interestingly, however, such variation is rather modest, and the Tiwanaku seem to have been a lot less interested in expending considerable labour and resources in burial facilities than their pre-Columbian contemporaries of many parts of the Central Andes.

Highly Monodisperse Colloidal Magnesium Nanoparticles by Room Temperature Digestive Ripening

Nanoclusters of 25 nm sized Mg-THF have been prepared by the solvated metal atom dispersion method. Room-temperature digestive ripening of these nanoclusters in the presence of hexadecylamine (HDA) resulted in highly monodisperse colloidal Mg-HDA nanoparticles of 2.8 ± 0.2 nm. An insight into the room-temperature digestive ripening process was obtained by studying the disintegration of clusters for various Mg:HDA ratios. The Mg colloids are quite stable with respect to precipitation of particles under Ar atmosphere. Using this procedure, pure Mg(0) nanopowders were obtained in gram scale quantities. The Mg powder precipitated from the colloid was fully hydrided at 33 bar and 118 °C. Initial desorption of H2 from samples of MgH2 was achieved at a remarkably low temperature, 115 °C compared to >350 °C in bulk Mg, demonstrating the importance of the size on the desorption temperatures.

En sjukdom af högst elakt släckte : Återfallsfebern på Sveaborg och i Karlskrona 1788-1790

Sommaren 1788 drabbades den svenska flottan av en svårartad febersjukdom. Febern, som senare definierats som febris recurrens el. återfallsfeber, hade sitt ursprung i den ryska flottan. Besättningen ombord skeppet Vladislav, krigsbytet från slaget vid Hogland, bar på ett stort antal smittade klädlöss. Efter flottans ankomst till Sveaborg spred sig sjukdomen snabbt bland manskapet, men även bland fästningens garnison. Förhållandena inom militären, både inom lantarmén och framför allt inom flottan, var gynnsamma för epidemiers spridning. De trånga utrymmena, den ensidiga kosten, det undermåliga dricksvattnet, den bristande hygienen: allt gynnade uppkomsten och spridningen av olika epidemier. Manskapets försämrade allmäntillstånd gjorde, att sjukdomarna blev mera förödande än vad de i andra förhållanden skulle ha varit. Bristen på manskap och material under Gustav III:s ryska krig var enormt, bl.a. var bristen på medicinsk personal och -utrustning skriande. Då flottan och armén drabbades av en epidemi av katastrofala dimensioner stod myndigheterna hjälplösa. Epidemin visaqr tydligt hur illa förberett hela kriget var och hur misskött flottans sjukvård var. På Sveaborg var förhållandena fruktansvärda. Halva garnisonen uppges ha avlidit, och det låg travar av lik överallt. Kaserner m.fl. byggnader adapterades till provisoriska lasarett och det rådde brist på allt. De medicinska myndigheterna representerades av den till fästningen skickade andra fältläkaren, som tillsammans med läkarna på fästningen gjorde sitt bästa i enlighet med tidens vårdmetoder. Då den svenska örlogsflottan i november seglat över tilll Karlskrona spred sig epidemin i staden. Sjukdomen grasserade också bland de civila. Då sjukdomens orsak och utbredningssätt var okända, kunde man varken hindra epidemin från att spridas eller genomföra adekvata vårdmetoder. Tvärtom, med de hemförlovade båtsmännen spred sig sjukdomen även till de övriga delarna av riket. Under 1789 var flottan p.g.a. de många sjukdomsfallen närmast operationsoduglig. Under vårvintern och våren 1790 avtog epidemin. Epidemin var ett svårt medicinskt problem. För att utreda situationen i Karlskrona skickade den tillförordnade regeringen, utredningskommissionen och Collegium medicum sina egna representanter till staden. De olika läkarnas sjukdomssyner grundade sig främst på tron om sjukdomars uppkomst genom miasma och förbättrandet av luftkvaliteten sågs som en väsentlig vårdform. I arbetet jämförs de olika myndigheternas och några av de på platsen varande läkarnas syn på sjukdomens art, dess orsaker och ursprung. De flesta härleder sjukdomen till den ryska flottan, och nämner någon form av smitta. Som främsta sjukdomsorsak nämns dock miasma och de rekommenderade vårdformerna representerade den humoralpatologiska synen. Förste amiralitetsläkaren Arvid Faxe representerar dock en annan åsikt, i det att han enbart tror på sjukdomens överföring via smitta. Epidemin var också ett politiskt problem. Epidemin var en lokal angelägenhet ända till dess att flottans operationer hämmades av manskapsbristen, varefter den blev ett ärende på högsta nivå. Kungen ingrep sommaren 1789 genom att grunda en kommision med rätt vidsträckta befogenheter. I Karlskrona verkar de militära myndigheterna och läkarna ha misstrott och skuldsatt varandra för katastrofen, och förhållandet mellan de till staden sända utredarna och militärerna var likaså inflammerat. Genom källorna återspeglas rivalitet, avund och inbördes konkurrens. Personalbristen var svår, och den skyldiga söktes utanför den egna kretsen. Den danskfödde apotekaren med sina påstott otjänliga mediciner blev en ypperlig syndabock. Örlogsflottan beräknas i sjukdomar ha förlorat omkring 10.000 man i döda, huvudsakligen i Karlskrona (civila inberäknade). Armén och Skärgårdsflottan uppges likadeles ha mist omkring 10.000 man, medan antalet i strid stupade armésoldater endast var ca 1500. Sammanlagt antas alltså ca 20.000 människor ha mist livet; både i återfallsfeber, men även i andra, samtidigt grasserande farsoter. I denna siffra är inte de övriga delarna av riket inberäknade. Epidemin i fråga kan alltså på goda grunder anses vara det svenska 1700-talets största medicinska katastrof.

Universal Access-NY User’s Guide

What is Universal Access-NY? Universal Access-NY is a complete online planning toolkit, www.UniversalAccessNY.org, where a One-Stop Delivery System can assess its practices, and develop work plans to improve physical and programmatic accessibility for all One-Stop customers. This web site and manual was developed by Cornell University’s Employment and Disability Institute, through the support and guidance of the New York State Department of Labor, with funding from two U.S. Department of Labor Work Incentive Grants (WIG 1 and 2). This web site was designed for use in a collaborative manner, bringing together One-Stop personnel, agency partners, business leaders and customers with disabilities. Universal Access-NY supports continuous improvement, with features that encourage multiple uses and incremental systems change.

Promising Practices: Ensuring Choice Under the Ticket to Work Program - The Indiana PABSS Approach

The Ticket to Work program offered disabled and blind social security beneficiaries the promise of greater choice when selecting a vocational rehabilitation provider. With the issuance of Transmittal #17, much of the opportunity to choose a provider was removed. The Protection and Advocacy agency in Indiana took steps to protect the rights of disabled and blind beneficiaries to choose providers in the face of this significant policy change. Learn what was done to protect the rights and ability of beneficiaries to seek and choose vocational rehabilitation providers.

An (O)over-tilde(mn) Gomory-Hu Tree Construction Algorithm for Unweighted Graphs

We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V, E). The expected running time of our algorithm is (O) over tilde (mc) where vertical bar E vertical bar = m and c is the maximum u-v edge connectivity, where u, v is an element of V. When the input graph is also simple (i.e., it has no parallel edges), then the u-v edge connectivity for each pair of vertices u and v is at most n - 1; so the expected run-ning time of our algorithm for simple unweighted graphs is (O) over tilde (mn). All the algorithms currently known for constructing a Gomory-Hu tree [8, 9] use n - 1 minimum s-t cut (i.e., max flow) subroutines. This in conjunction with the current fastest (O) over tilde (n(20/9)) max flow algorithm due to Karger and Levine[11] yields the current best running time of (O) over tilde (n(20/9)n) for Gomory-Hu tree construction on simple unweighted graphs with m edges and n vertices. Thus we present the first (O) over tilde (mn) algorithm for constructing a Gomory-Hu tree for simple unweighted graphs. We do not use a max flow subroutine here; we present an efficient tree packing algorithm for computing Steiner edge connectivity and use this algorithm as our main subroutine. The advantage in using a tree packing algorithm for constructing a Gomory-Hu tree is that the work done in computing a minimum Steiner cut for a Steiner set S subset of V can be reused for computing a minimum Steiner cut for certain Steiner sets S' subset of S.

On the Arrangement of Cliques in Chordal Graphs with respect to the Cuts

A cut (A, B) (where B = V - A) in a graph G = (V, E) is called internal if and only if there exists a vertex x in A that is not adjacent to any vertex in B and there exists a vertex y is an element of B such that it is not adjacent to any vertex in A. In this paper, we present a theorem regarding the arrangement of cliques in a chordal graph with respect to its internal cuts. Our main result is that given any internal cut (A, B) in a chordal graph G, there exists a clique with kappa(G) + vertices (where kappa(G) is the vertex connectivity of G) such that it is (approximately) bisected by the cut (A, B). In fact we give a stronger result: For any internal cut (A, B) of a chordal graph, and for each i, 0 <= i <= kappa(G) + 1 such that vertical bar K-i vertical bar = kappa(G) + 1, vertical bar A boolean AND K-i vertical bar = i and vertical bar B boolean AND K-i vertical bar = kappa(G) + 1 - i. An immediate corollary of the above result is that the number of edges in any internal cut (of a chordal graph) should be Omega(k(2)), where kappa(G) = k. Prompted by this observation, we investigate the size of internal cuts in terms of the vertex connectivity of the chordal graphs. As a corollary, we show that in chordal graphs, if the edge connectivity is strictly less than the minimum degree, then the size of the mincut is at least kappa(G)(kappa(G)+1)/2 where kappa(G) denotes the vertex connectivity. In contrast, in a general graph the size of the mincut can be equal to kappa(G). This result is tight.

Correlation Between The Stability Of Carbonates In Ternary Ln2o3-H2o-Co2 Hydrothermal Systems And Lanthanide Systematics

Phase diagrams for ternary Ln2O3-H2O-CO2 systems for the entire lanthanide series (except promethium) were studied at temperatures in the range 100–950 °C and pressures up to 3000 bar. The phase diagrams obtained for the heavier lanthanides are far more complex, with the appearance of a number of stable carbonate phases. New carbonates isolated from lanthanide systems (Ln ≡ Tm, Yb, Lu) include Ln6(OH)4(CO3)7, Ln4(OH)6-(CO3)3, Ln2O(OH)2CO3, Ln6O2(OH)8(CO3)3 and Ln12O7(OH)10(CO3)6. Stable carbonate phases common to all the lighter lanthanides are hexagonal LnOHCO3 and hexagonal Ln2O2CO3. Ln2(CO3)3• 3H2O is stable from samarium onwards and orthorhombic LnOHCO3 is stable from gadolinium onwards. On the basis of the appearance of stable carbonates, four different groups of lanthanides were established: lanthanum to neodymium, promethium to europium, terbium to erbium and thulium to lutetium. Gadolinium is the connecting element between groups II and III. This is in accordance with the tetrad classification for f transition elements.

In Situ Phase Separation Following Dehydration in Bimetallic Sulfates: A Variable-Temperature X-Ray Diffraction Study

Phase separation resulting in a single-crystal-single-crystal transition accompanied by a polycrystalline phase following the dehydration of hydrated bimetallic sulfates [Na2Mn1.167(SO4)(2)S0.33O1.167 center dot 2H(2)O and K4Cd3-(SO4)(5)center dot 3H(2)O] has been investigated by in situ variable-temperature single-crystal X-ray diffraction. With two examples, we illustrate the possibility of generating structural frameworks following dehydration in bimetallic sulfates, which refer to the possible precursor phases at that temperature leading to the mineral formation. The room-temperature structure of Na2Mn1.167(SO4)(2)S0.33O1.167 center dot 2H(2)O is trigonal, space group R (3) over bar. On heating the crystal in situ on the diffractometer, the diffraction images display spherical spots and concentric rings suggesting phase separation, with the spherical spots getting indexed in a monoclinic space group, C2/c. The structure determination based on this data suggests the formation of Na2Mn(SO4)(2). However, the diffraction images from concentric rings could not be indexed. In the second example, the room-temperature structure is determined to be K4Cd3(SO4)(5)center dot 3H(2)O, crystallizing in a monoclinic space group, P2(1)/n. On heating the crystal in situ, the diffraction images collected also have both spherical spots and diffuse rings. The spherical spots could be indexed to a cubic crystal system, space group P2(1)3, and the structure is K4Cd3(SO4)(3). The possible mechanism for the phase transition in the dehydration regime resulting in this remarkable single-crystal to single-crystal transition with the appearance of a surrogate polycrystalline phase is proposed.

Self-Assembly of Molecular Prisms via Pt-3 Organometallic Acceptors and a Pt-2 Organometallic Clip

The design and two-component [2 + 3] self-assembly of a series of new organometallic molecular prisms (3a-d) are described. Assemblies 3a,b incorporate 4,4',4'-tris[ethynyl-trans-Pt(PEt3)(2)]triphenylamine (1a) containing a Pt-ethynyl functionality as tritopic planar acceptor and organic ``clips'' 2a and 2b, respectively [where 2a = 1,3-bis(3-pyridyl)isophthalic amide; 2b= 1,3-bis(ethynyl-3-pyridyl)benzene]. In a complementary approach all organic tritopic planar donor ligand 2c [2c 4,4',4'-tris(4-pyridylethynyl)triphenylamine] was assembled with all organometallic ``clip'', 1,8-bis[{trans-Pt(PEt3) (2)(NO3)}ethynyl]anthracene (1b), to obtain prism 3c. A organometallic carbon-centered acceptor, 1,1,1- tris[4-{trans-Pt(PEt3)(2)(NO3)}ethynylphenyl]ethane (1c), has been prepared, and its prism derivative (3d) using an organic `clip'' is prepared. Assemblies (3a-d) were characterized by multinuclear NMR spectroscopy, electrospray ionization mass spectroscopy, and elemental analysis. 3a-d showed fluorescence behavior in solution, and quenching of fluorescence intensity (3a,3c-d) was noticed upon addition of TNT (2,4,6-trinitrotoluene), a common constituent of many commercial explosives. A thin film of the assembly 3d made by spin coating of a solution of 3 x 10(-5) M in DMF on it 1 cm(2) quartz plate showed fluorescence response to the vapor of TNT.

Self-assembly of a Pd-II neutral molecular rectangle via a new organometallic Pd-2(II) molecular clip and oxygen donor linker

Two components self-assembly of a Pd-4 neutral molecular rectangle driven by Pd-O bond coordination has been achieved and this pi-electron rich rectangle shows fluorescence quenching in presence of nitroaromatics, which are the chemical signatures of many explosives.

Pond apple (Annona glabra L.) - Investigating novel mechanical control options

Pond apple usually occurs in swampy areas, but mechanical control may be a viable option in some locations during drier periods. Two machines, the Positrack™ and the Tracksaw™, have been trialled for initial kill rate, amount of follow-up control required, safety to field operators, cost-efficiency and selectivity (effect on native vegetation), compared to other control options. The Positrack™ is a tracked bobcat with a slasher-type attachment that cuts individual trees off near ground level and mulches them. It has no on-board herbicide application capability and requires an additional on-ground operator to apply herbicide by hand. The Tracksaw™ is a tracked mini-excavator with a chainsaw bar and spray applicator on the boom that cuts individual trees off near ground level and applies chemical immediately to the cut stump, requiring only a single operator. Initial trials were done in infestations of similar sizes and densities at the Daintree (Positrack™) and in Innisfail (Tracksaw™) in late 2009. Kill rates to date are 83% for Positrack™ mechanical, 95% for Positrack™ mechanical plus herbicide, and 78% for the Tracksaw™ combined treatment. If ongoing comparison proves either of these machines to be more cost effective, selective, and safer than traditional control methods, mechanical control methods may become more widely used.

Assessment and control of Bacillus cereus emetic toxin in food

Despite of improving levels of hygiene, the incidence of registered food borne disease has been at the same level for many years: there were 40 to 90 epidemics in which 1000-9000 persons contracted food poisoning through food or drinking water in Finland. Until the year 2004 salmonella and campylobacter were the most common bacterial causes of food borne diseases, but in years 2005-2006 Bacillus cereus was the most common. Similar developement has been published i.e. in Germany already in the 1990´s. One reason for this can be Bacillus cereus and its emetic toxin, cereulide. Bacillus cereus is a common environmental bacterium that contaminates raw materials of food. Otherwise than salmonella and campylobacter, Bacillus cereus is a heat resistant bacterium, capable of surviving most cooking procedures due to the production of highly thermo resistant spores. The food involved has usually been heat treated and surviving spores are the source of the food poisoning. The heat treatment induces germination of the spore and the vegetative cells then produce toxins. This doctoral thesis research focuses on developing methods for assessing and eliminating risks to food safety by cereulide producing Bacillus cereus. The biochemistry and physiology of cereulide production was investigated and the results were targeted to offer tools for minimizing toxin risk in food during the production. I developed methods for the extraction and quantitative analysis of cereulide directly from food. A prerequisite for that is knowledge of the chemical and physical properties of the toxin. Because cereulide is practically insoluble in water, I used organic solvents; methanol, ethanol and pentane for the extraction. For extraction of bakery products I used high temperature (100C) and pressure (103.4 bars). Alternaties for effective extraction is to flood the plain food with ethanol, followed by stationary equilibration at room temperature. I used this protocol for extracting cereulide from potato puree and penne. Using this extraction method it is also possible also extract cereulide from liquid food, like milk. These extraction methods are important improvement steps for studying of Bacillus cereus emetic food poisonings. Prior my work, cereulide extraction was done using water. As the result, the yield was poor and variable. To investigate suspected food poisonings, it is important to show actual toxicity of the incriminated food. Many toxins, but not cereulide, inactivate during food processing like heating. The next step is to identify toxin by chemical methods. I developed with my colleague Maria Andesson a rapid assay for the detection of cereulide toxicity, within 5 to 15 minutes. By applying this test it is possible to rapidly detect which food was causing the food poisoning. The chemical identification of cereulide was achieved using mass spectrometry. I used cereulide specific molecular ions, m/z (+/-0.3) 1153.8 (M+H+), 1171.0 (M+NH4+), 1176.0 (M+Na+) and 1191.7 (M+K+) for reliable identification. I investigated foods to find out their amenability to accumulate cereulide. Cereulide was formed high amounts (0.3 to 5.5 microg/g wet wt) when of cereulide producing B. cereus strains were present in beans, rice, rice-pastry and meat-pastry, if stored at non refrigerated temperatures (21-23C). Rice and meat pastries are frequently consumed under conditions where no cooled storage is available e.g. picnics and outdoor events. Bacillus cereus is a ubiquitous spore former and is therefore difficult to eliminate from foods. It is therefore important to know which conditions will affect the formation of cereulide in foods. My research showed that the cereulide content was strongly (10 to 1000 fold differences in toxin content) affected by the growth environment of the bacterium. Storage of foods under nitrogen atmosphere (> 99.5 %) prevented the production of cereulide. But when also carbon dioxide was present, minimizing the oxygen contant (< 1%) did not protect the food from formation of cereulide in preliminary experiments. Also food supplements affected cereulide production at least in the laboratory. Adding free amino acids, leucine and valine, stimulated cereulide production 10 to 20 fold. In peptide bonded form these amino acids are natural constituents in all proteins. Interestingly, adding peptide bonded leucine and valine had no significant effect on cereulide production. Free amino acids leucine and valine are approved food supplements and widely used as flawour modifiers in food technology. My research showed that these food supplements may increase food poisoning risk even though they are not toxic themselves.

New nondestructive method for three-dimensional photoelasticity

A new set of equations describing completely the optical phenomena in a model involving continuous rotation of secondary axes and secondary principal-stress differences are obtained. These are solved by Peano-Baker method using experimentally determined characteristic parameters for several wavelengths of light. Experimental verifications are obtained for a rectangular bar subjected to combined torsion and tension. Paper was presented at Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13–18, 1973.